diff --git a/httpcore/_async/http11.py b/httpcore/_async/http11.py
index 7ad3664..32fa3a6 100644
--- a/httpcore/_async/http11.py
+++ b/httpcore/_async/http11.py
@@ -20,6 +20,7 @@ from .._exceptions import (
     ConnectionNotAvailable,
     LocalProtocolError,
     RemoteProtocolError,
+    WriteError,
     map_exceptions,
 )
 from .._models import Origin, Request, Response
@@ -84,10 +85,21 @@ class AsyncHTTP11Connection(AsyncConnectionInterface):
 
         try:
             kwargs = {"request": request}
-            async with Trace("send_request_headers", logger, request, kwargs) as trace:
-                await self._send_request_headers(**kwargs)
-            async with Trace("send_request_body", logger, request, kwargs) as trace:
-                await self._send_request_body(**kwargs)
+            try:
+                async with Trace(
+                    "send_request_headers", logger, request, kwargs
+                ) as trace:
+                    await self._send_request_headers(**kwargs)
+                async with Trace("send_request_body", logger, request, kwargs) as trace:
+                    await self._send_request_body(**kwargs)
+            except WriteError:
+                # If we get a write error while we're writing the request,
+                # then we supress this error and move on to attempting to
+                # read the response. Servers can sometimes close the request
+                # pre-emptively and then respond with a well formed HTTP
+                # error response.
+                pass
+
             async with Trace(
                 "receive_response_headers", logger, request, kwargs
             ) as trace:
diff --git a/httpcore/_sync/http11.py b/httpcore/_sync/http11.py
index edcce72..0cc100e 100644
--- a/httpcore/_sync/http11.py
+++ b/httpcore/_sync/http11.py
@@ -20,6 +20,7 @@ from .._exceptions import (
     ConnectionNotAvailable,
     LocalProtocolError,
     RemoteProtocolError,
+    WriteError,
     map_exceptions,
 )
 from .._models import Origin, Request, Response
@@ -84,10 +85,21 @@ class HTTP11Connection(ConnectionInterface):
 
         try:
             kwargs = {"request": request}
-            with Trace("send_request_headers", logger, request, kwargs) as trace:
-                self._send_request_headers(**kwargs)
-            with Trace("send_request_body", logger, request, kwargs) as trace:
-                self._send_request_body(**kwargs)
+            try:
+                with Trace(
+                    "send_request_headers", logger, request, kwargs
+                ) as trace:
+                    self._send_request_headers(**kwargs)
+                with Trace("send_request_body", logger, request, kwargs) as trace:
+                    self._send_request_body(**kwargs)
+            except WriteError:
+                # If we get a write error while we're writing the request,
+                # then we supress this error and move on to attempting to
+                # read the response. Servers can sometimes close the request
+                # pre-emptively and then respond with a well formed HTTP
+                # error response.
+                pass
+
             with Trace(
                 "receive_response_headers", logger, request, kwargs
             ) as trace:

diff --git a/tests/_async/test_connection.py b/tests/_async/test_connection.py
index 8b29942..b6ee0c7 100644
--- a/tests/_async/test_connection.py
+++ b/tests/_async/test_connection.py
@@ -9,10 +9,13 @@ from httpcore import (
     SOCKET_OPTION,
     AsyncHTTPConnection,
     AsyncMockBackend,
+    AsyncMockStream,
     AsyncNetworkStream,
     ConnectError,
     ConnectionNotAvailable,
     Origin,
+    RemoteProtocolError,
+    WriteError,
 )
 
 
@@ -83,7 +86,109 @@ async def test_concurrent_requests_not_available_on_http11_connections():
                 await conn.request("GET", "https://example.com/")
 
 
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
 @pytest.mark.anyio
+async def test_write_error_with_response_sent():
+    """
+    If a server half-closes the connection while the client is sending
+    the request, it may still send a response. In this case the client
+    should successfully read and return the response.
+
+    See also the `test_write_error_without_response_sent` test above.
+    """
+
+    class ErrorOnRequestTooLargeStream(AsyncMockStream):
+        def __init__(self, buffer: typing.List[bytes], http2: bool = False) -> None:
+            super().__init__(buffer, http2)
+            self.count = 0
+
+        async def write(
+            self, buffer: bytes, timeout: typing.Optional[float] = None
+        ) -> None:
+            self.count += len(buffer)
+
+            if self.count > 1_000_000:
+                raise WriteError()
+
+    class ErrorOnRequestTooLarge(AsyncMockBackend):
+        async def connect_tcp(
+            self,
+            host: str,
+            port: int,
+            timeout: typing.Optional[float] = None,
+            local_address: typing.Optional[str] = None,
+            socket_options: typing.Optional[typing.Iterable[SOCKET_OPTION]] = None,
+        ) -> AsyncMockStream:
+            return ErrorOnRequestTooLargeStream(list(self._buffer), http2=self._http2)
+
+    origin = Origin(b"https", b"example.com", 443)
+    network_backend = ErrorOnRequestTooLarge(
+        [
+            b"HTTP/1.1 413 Payload Too Large\r\n",
+            b"Content-Type: plain/text\r\n",
+            b"Content-Length: 37\r\n",
+            b"\r\n",
+            b"Request body exceeded 1,000,000 bytes",
+        ]
+    )
+
+    async with AsyncHTTPConnection(
+        origin=origin, network_backend=network_backend, keepalive_expiry=5.0
+    ) as conn:
+        content = b"x" * 10_000_000
+        response = await conn.request("POST", "https://example.com/", content=content)
+        assert response.status == 413
+        assert response.content == b"Request body exceeded 1,000,000 bytes"
+
+
+@pytest.mark.anyio
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
+async def test_write_error_without_response_sent():
+    """
+    If a server fully closes the connection while the client is sending
+    the request, then client should raise an error.
+
+    See also the `test_write_error_with_response_sent` test above.
+    """
+
+    class ErrorOnRequestTooLargeStream(AsyncMockStream):
+        def __init__(self, buffer: typing.List[bytes], http2: bool = False) -> None:
+            super().__init__(buffer, http2)
+            self.count = 0
+
+        async def write(
+            self, buffer: bytes, timeout: typing.Optional[float] = None
+        ) -> None:
+            self.count += len(buffer)
+
+            if self.count > 1_000_000:
+                raise WriteError()
+
+    class ErrorOnRequestTooLarge(AsyncMockBackend):
+        async def connect_tcp(
+            self,
+            host: str,
+            port: int,
+            timeout: typing.Optional[float] = None,
+            local_address: typing.Optional[str] = None,
+            socket_options: typing.Optional[typing.Iterable[SOCKET_OPTION]] = None,
+        ) -> AsyncMockStream:
+            return ErrorOnRequestTooLargeStream(list(self._buffer), http2=self._http2)
+
+    origin = Origin(b"https", b"example.com", 443)
+    network_backend = ErrorOnRequestTooLarge([])
+
+    async with AsyncHTTPConnection(
+        origin=origin, network_backend=network_backend, keepalive_expiry=5.0
+    ) as conn:
+        content = b"x" * 10_000_000
+        with pytest.raises(RemoteProtocolError) as exc_info:
+            await conn.request("POST", "https://example.com/", content=content)
+        assert str(exc_info.value) == "Server disconnected without sending a response."
+
+
+@pytest.mark.anyio
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
 async def test_http2_connection():
     origin = Origin(b"https", b"example.com", 443)
     network_backend = AsyncMockBackend(
diff --git a/tests/_sync/test_connection.py b/tests/_sync/test_connection.py
index 9e0c403..37c82e0 100644
--- a/tests/_sync/test_connection.py
+++ b/tests/_sync/test_connection.py
@@ -9,10 +9,13 @@ from httpcore import (
     SOCKET_OPTION,
     HTTPConnection,
     MockBackend,
+    MockStream,
     NetworkStream,
     ConnectError,
     ConnectionNotAvailable,
     Origin,
+    RemoteProtocolError,
+    WriteError,
 )
 
 
@@ -83,7 +86,109 @@ def test_concurrent_requests_not_available_on_http11_connections():
                 conn.request("GET", "https://example.com/")
 
 
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
 
+def test_write_error_with_response_sent():
+    """
+    If a server half-closes the connection while the client is sending
+    the request, it may still send a response. In this case the client
+    should successfully read and return the response.
+
+    See also the `test_write_error_without_response_sent` test above.
+    """
+
+    class ErrorOnRequestTooLargeStream(MockStream):
+        def __init__(self, buffer: typing.List[bytes], http2: bool = False) -> None:
+            super().__init__(buffer, http2)
+            self.count = 0
+
+        def write(
+            self, buffer: bytes, timeout: typing.Optional[float] = None
+        ) -> None:
+            self.count += len(buffer)
+
+            if self.count > 1_000_000:
+                raise WriteError()
+
+    class ErrorOnRequestTooLarge(MockBackend):
+        def connect_tcp(
+            self,
+            host: str,
+            port: int,
+            timeout: typing.Optional[float] = None,
+            local_address: typing.Optional[str] = None,
+            socket_options: typing.Optional[typing.Iterable[SOCKET_OPTION]] = None,
+        ) -> MockStream:
+            return ErrorOnRequestTooLargeStream(list(self._buffer), http2=self._http2)
+
+    origin = Origin(b"https", b"example.com", 443)
+    network_backend = ErrorOnRequestTooLarge(
+        [
+            b"HTTP/1.1 413 Payload Too Large\r\n",
+            b"Content-Type: plain/text\r\n",
+            b"Content-Length: 37\r\n",
+            b"\r\n",
+            b"Request body exceeded 1,000,000 bytes",
+        ]
+    )
+
+    with HTTPConnection(
+        origin=origin, network_backend=network_backend, keepalive_expiry=5.0
+    ) as conn:
+        content = b"x" * 10_000_000
+        response = conn.request("POST", "https://example.com/", content=content)
+        assert response.status == 413
+        assert response.content == b"Request body exceeded 1,000,000 bytes"
+
+
+
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
+def test_write_error_without_response_sent():
+    """
+    If a server fully closes the connection while the client is sending
+    the request, then client should raise an error.
+
+    See also the `test_write_error_with_response_sent` test above.
+    """
+
+    class ErrorOnRequestTooLargeStream(MockStream):
+        def __init__(self, buffer: typing.List[bytes], http2: bool = False) -> None:
+            super().__init__(buffer, http2)
+            self.count = 0
+
+        def write(
+            self, buffer: bytes, timeout: typing.Optional[float] = None
+        ) -> None:
+            self.count += len(buffer)
+
+            if self.count > 1_000_000:
+                raise WriteError()
+
+    class ErrorOnRequestTooLarge(MockBackend):
+        def connect_tcp(
+            self,
+            host: str,
+            port: int,
+            timeout: typing.Optional[float] = None,
+            local_address: typing.Optional[str] = None,
+            socket_options: typing.Optional[typing.Iterable[SOCKET_OPTION]] = None,
+        ) -> MockStream:
+            return ErrorOnRequestTooLargeStream(list(self._buffer), http2=self._http2)
+
+    origin = Origin(b"https", b"example.com", 443)
+    network_backend = ErrorOnRequestTooLarge([])
+
+    with HTTPConnection(
+        origin=origin, network_backend=network_backend, keepalive_expiry=5.0
+    ) as conn:
+        content = b"x" * 10_000_000
+        with pytest.raises(RemoteProtocolError) as exc_info:
+            conn.request("POST", "https://example.com/", content=content)
+        assert str(exc_info.value) == "Server disconnected without sending a response."
+
+
+
+@pytest.mark.filterwarnings("ignore::pytest.PytestUnraisableExceptionWarning")
 def test_http2_connection():
     origin = Origin(b"https", b"example.com", 443)
     network_backend = MockBackend(

Handle HTTP/1.1 half-closed connections gracefully.
There's an HTTP/1.1 case that can occur where...

* The client starts sending a request.
* The server half-closes the connection.
* The server sends a response, such as an HTTP 413 Content Too Large.

Currently our behaviour here is that we'll see a `WriteError` occur here and never get a response.
A more graceful behaviour is handle this case, and return the 413 response.

Prompted via https://github.com/encode/httpx/discussions/2503.

*A follow up question to this will be... is there an equivalent to this for HTTP/2 streams? But let's only consider that once we've dealt with this as a precursor.*
tests/_async/test_connection.py::test_write_error_with_response_sent[asyncio] tests/_async/test_connection.py::test_write_error_without_response_sent[asyncio] tests/_async/test_connection.py::test_write_error_with_response_sent[trio] tests/_async/test_connection.py::test_write_error_without_response_sent[trio] tests/_sync/test_connection.py::test_write_error_with_response_sent tests/_sync/test_connection.py::test_write_error_without_response_sent
tests/_async/test_connection.py::test_http_connection[asyncio] tests/_async/test_connection.py::test_concurrent_requests_not_available_on_http11_connections[asyncio] tests/_async/test_connection.py::test_http2_connection[asyncio] tests/_async/test_connection.py::test_request_to_incorrect_origin[asyncio] tests/_async/test_connection.py::test_connection_retries[asyncio] tests/_async/test_connection.py::test_connection_retries_tls[asyncio] tests/_async/test_connection.py::test_uds_connections[asyncio] tests/_async/test_connection.py::test_http_connection[trio] tests/_async/test_connection.py::test_concurrent_requests_not_available_on_http11_connections[trio] tests/_async/test_connection.py::test_http2_connection[trio] tests/_async/test_connection.py::test_request_to_incorrect_origin[trio] tests/_async/test_connection.py::test_connection_retries[trio] tests/_async/test_connection.py::test_connection_retries_tls[trio] tests/_async/test_connection.py::test_uds_connections[trio] tests/_sync/test_connection.py::test_http_connection tests/_sync/test_connection.py::test_concurrent_requests_not_available_on_http11_connections tests/_sync/test_connection.py::test_http2_connection tests/_sync/test_connection.py::test_request_to_incorrect_origin tests/_sync/test_connection.py::test_connection_retries tests/_sync/test_connection.py::test_connection_retries_tls tests/_sync/test_connection.py::test_uds_connections