In the first instance, while the impossible trinity is usually stated in terms of an independent monetary policy, it should more accurately be stated in terms of independent macroeconomic policy, for when a currency comes under serious pressure, typically both monetary and fiscal policy have to adjust if the exchange rate is to be maintained.
Admittedly, in some large emerging countries, in particular in China, private sector liabilities have risen sharply in the past decade as a share of GDP, raising the risk of a future adjustment that may, at some stage, have adverse consequences on not just local but also global economic growth.