Hurricane Irma barreled through Gainesville, Fla., in 2017, displacing some of the clients Faye Feazell worked with as a home health aide. Ms. Feazell, unsure how she would make her monthly mortgage payments, called her mortgage company for help.

She said the company, AmeriHome Mortgage Co., told her not to worry: She could skip payments for 90 days. But three months later, when she called to find out about resuming payments, she learned she was being foreclosed on, she said. The AmeriHome employee she spoke to didn’t know...