Why do emerging market economies simultaneously hold very high levels of international reserves and foreign liabilities? Moreover, why, even with such huge amounts of international reserves, did countries barely use them during the Global Financial Crisis? I argue that including international reserves as an implicit collateral for external borrowing in a small open economy model subject to exogenous financial shocks can explain both of these puzzling facts. I find that the model can obtain ratios of international reserves and net foreign liabilities to GDP similar to those of Latin American countries. Additionally, the optimal policy implies that the government accumulates international reserves before a sudden stop and that there is a small depletion during it. Finally, an alternative policy of keeping international reserves constant at the average level yields results very similar to those of the optimal policy during sudden stops, highlighting the stabilizing role of international reserves even if central banks do not use them.