Shelter-in-place policies and the closure of non-essential workplaces intended to disrupt transmission of the SARS-COV-2 virus are effective approaches to combating COVID-19. They have, however, caused record levels of unemployment in the United States, raising questions of whether mitigation is more societally damaging than the disease. Here we use a coupled epidemiological-economic model to estimate the impact on employment of an unmitigated, business-as-usual approach to the pandemic. We compared unemployment between March-August 2020 in ten Californian socio-economic systems (SESs) to unemployment forecast by a model of industrial sector inter-dependencies subjected to unmitigated outbreaks of COVID-19. We found that economic losses are unavoidable because disease-driven losses propagate economically through SESs, amplifying losses to the disease. While model forecasts are generally lower than actual unemployment, jobs savings would come at the cost of greatly increased worker mortality. The costs would also be disproportionately greater among smaller and inland SESs.