We present a model in which temporary shocks can permanently scar the economy's productive capacity. Unemployed workers lose skill and are expensive to retrain, generating multiple steady state unemployment rates. Large temporary shocks push the economy into a liquidity trap, generating deflation. With nominal wages unable to adjust freely, real wages rise, reducing hiring and catapulting the economy toward the high-unemployment steady state. Even after a short-lived liquidity trap, the economy recovers slowly at best; at worst, it falls into a permanent unemployment trap. Because monetary policy may be powerless to escape such a trap ex post, it is especially important to avoid it ex ante: policy should be preventive rather than curative. The model can quantitatively account for the slow recovery in the United States following the Great Recession. The model also suggests that a lack of swift monetary accommodation by the ECB can help explain stagnation in the European periphery.