We construct a multi-sector search and matching model where the unemployed receive idiosyncratic productivity shocks that make working in certain sectors more productive than in the others. Agents must decide which sector to search in and face moving costs when leaving their current sector for another. In this environment, unemployment is associated with an additional risk: low future wages if mobility costs preclude search in the appropriate sector. This introduces a new role for unemployment benefits—productivity insurance while unemployed. Analytically, we characterize two competing effects of benefits on productivity, a moral hazard effect and a consumption effect. In a stylized quantitative analysis, we show that the consumption effect dominates, so that unemployment benefits increase per-worker productivity. We also analyze the welfare-maximizing benefit level and find that it decreases as moving costs increase.