Allie and Chris Lyons, the owners of a popular farm-to-table restaurant called Table 20 in Cartersville, Ga., have done the math. In two weeks, they expect to have just $6,000 in cash, after covering payroll, insurance and rent.

The first coronavirus infections in the Cartersville area were confirmed on March 11. Amid calls for social distancing and with sales plummeting, the couple on Monday laid off all but two of their dozen employees. They have asked their landlord and lenders for relief. They have canceled orders on everything...