Grace Rhodes was getting worried last month as she watched the coronavirus tear through New York and Chicago. But her 8,000-person hometown in southern Illinois still had no reported cases, and her boss at her pharmacy job assured her: “It’ll never get here.” Now it has. A new wave of coronavirus cases is spreading deep into rural corners of the country where people once hoped their communities might be shielded because of their isolation from hard-hit urban centers and the natural social distancing of life in the countryside. The coronavirus has officially reached nearly three-quarters of the country’s rural counties,...