We study financial panics in a small open economy with floating exchange rates. In our model, bank runs trigger a decline in domestic wealth and a currency depreciation. Runs are more likely when banks have dollar debt. Dollar debt emerges endogenously in response to the precautionary motive of domestic savers: dollar savings provide insurance against crises; so when crises are possible it becomes relatively more expensive for banks to borrow in local currency, which gives them an incentive to issue dollar debt. This feedback between aggregate risk and savers’ behavior can generate multiple equilibria, with the bad equilibrium characterized by financial dollarization and the possibility of bank runs. A domestic lender of last resort can eliminate the bad equilibrium, but interventions need to be fiscally credible. Holding foreign currency reserves hedges the fiscal position of the government and enhances its credibility, thus improving financial stability.