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We model sudden stops in a small open economy as rare discrete events precipitated by increases in the world risk-free rate. When external debt is large, the model exhibits multiple equilibria, one where external debt and consumption remain high, and one with a collapse in external debt and consumption. Private agents delever following an increase in the world interest rate, but they fail to internalize the impact of deleveraging on the price of collateral. For high levels of debt, even a small increase in the world interest rate can eliminate the high debt equilibrium and the economy experiences a sudden stop. The central bank can use foreign exchange intervention to prevent the sudden stop. If reserves cannot be borrowed, optimal policy is to "lean against the wind", buying foreign reserves ex-ante when private borrowing is high and selling them after an interest rate shock when private agents are deleveraging.