We study the interaction between two large income replacement programs in the United States: Unemployment Insurance (UI) and Social Security Disability Insurance (DI). We start by studying empirically the relationship between UI benefit durations and the number of DI applications and beneficiaries. Using variation in the timing and magnitude of UI extensions across states during the Great Recession, we find that UI extensions are associated with declines in DI applications. To obtain causal inference, we use two identification strategies. First, we exploit the sharp and unexpected decline in benefit durations in Missouri in April 2011, and show that it lead to a sizable increase in DI applications. Second, we use a border discontinuity design and find that the number of DI beneficiaries decreases on the side of the border that extends benefit durations. Motivated by these findings and to understand their implications for policy design, we construct a search model of the labor market with worker heterogeneity in health and skills. In times of low job finding rates, marginal workers claim DI as opposed to UI. The relative generosities of UI and DI programs affects who uses which program. In particular, extending the duration of UI benefits limits the number of unemployed that use DI to replace lost income, keeping more workers attached to the labor force. Such extensions also lead to compositional changes in the labor force, drawing in people with worse health conditions and lower productivity, thereby putting downward pressure on job finding rates. We use the calibrated model, which is quantitatively consistent with the empirical findings, to quantify these tradeoffs and evaluate the implications of the program substitution for policy design and labor market outcomes.