This phenomenon will not happen if there are financial frictions and borrowing constraints in East which prevent the real interest rate from rising or the borrowing demand from being satisfied. In that case we might even observe that the flow of capital is reversed, from East to West.
This is the so-called Lucas paradox; it’s what we are currently observing, for example, in some eastern Asian economies, notably in China, and what we saw in western Europe in the 1950s and 1960s. In central and eastern European countries, there does not seem to be such a paradox.