Under federal-state law workers who quit a job are not entitled to receive unemployment insurance benefits. To show how the existence of the uninsured affects wages and employment, I extend an equilibrium search model to account for two types of unemployed workers: those who are currently receiving unemployment benefits and for whom an increase in unemployment benefits reduces the incentive to work, and those who are currently not insured. For these, work provides an added value in the form of future eligibility, and an increase in unemployment benefits increases their willingness to work. Incorporating both types into a search model permits me to solve analytically for the endogenous wage dispersion and insurance rate in the economy. I show that, in general equilibrium when firms adjust their job creation margin, the wage dispersion is reduced and the overall effect of benefits can be signed: higher unemployment benefits increase average wages and decrease the vacancy-to-unemployment ratio.