A new virus had rapidly spread across the globe and Tuomey Healthcare System in South Carolina couldn’t get more protective masks for its hospital workers. A global run on them had created a shortage.

That was the 2009 “swine flu.” Tuomey later stockpiled protective gear, but over the years didn’t replenish some expired items. This year, it found that elastic bands on some of its masks were brittle. One snapped when an official tried it on.

The...