Firms in emerging markets are exposed to severe financial frictions and credit constraints, that are exacerbated by the sudden stop of capital inflows. Can monetary policy offset this external credit squeeze? We show that although this may be the case during moderate contractions (or in partial equilibrium), the expansionary effect of monetary policy vanishes during severe external crises. The exchange rate jumps to reduce the dollar value of domestic collateral until equilibrium in domestic financial markets is consistent with the external constraint. An expansionary monetary policy in this context raises the value of domestic collateral but it exacerbates the exchange rate depreciation (beyond the standard interest parity effect) and has little effect on aggregate activity. However there is a dynamic linkage between monetary policy and sudden stops. The anticipation of a dogged defense of the exchange rate worsens the consequences of sudden stops by distorting the private sector incentive to take precautions against these shocks. For similar general equilibrium reasons, dollarization of liabilities has limited impact during a sudden stop, but it has significant underinsurance consequences.