The coronavirus pandemic has severely impacted emerging markets by generating a large death toll, deep recessions, and a wave of sovereign defaults. We study this compound health, economic, and debt crisis and its mitigation by integrating epidemiological dynamics into a sovereign default model. The epidemic leads to an urgent need for social distancing measures, a large drop in economic activity, and a protracted debt crisis. The presence of default risk restricts fiscal space and presents emerging markets with a trade-off between mitigation of the pandemic and fiscal distress. A quantitative analysis of our model accounts well for the dynamics of deaths, social distance measures, and sovereign spreads in Latin America. In the model, the welfare cost of the pandemic is higher because of financial market frictions: about a third of the cost comes from default risk, compared with a version of the model with perfect financial markets. We study debt relief programs through counterfactuals and find a compelling case for their implementation, as they deliver large social gains.