Overseeing sober living homes for newly recovering drug addicts is difficult in the best of times. But the endless shutdowns have created conditions that are challenging for healthy people, let alone those who are fresh out of rehab, vulnerable, and still reeling.

Matt Royce, 35, oversees seven sober-living homes in Minneapolis. All of his houses, each holding between 9 and 13 people, have been “pretty full the whole time.”

No overdose deaths had occurred in his homes in almost three years, but last summer he lost two people, while another...