For the past week, Robert Tierney Jr. has been registering patients at a Northern California hospital in the mornings and checking out possible rentals after work, trying to count his blessings even though his house is one of the more than 1,000 destroyed in a deadly wildfire.

Tierney is among dozens of staff members, including doctors, nurses and others, at Dignity Health Mercy Medical Center in Redding keeping the hospital running despite losing their homes to the flames.

Tierney, 57, choked up briefly as he recalled the moment he learned from a kid on a bicycle that his house and belongings...