CHICO, Calif. — Within hours of the flames igniting in Northern California last week, an instant new homeless crisis was born. In a state already suffering an acute housing shortage, the fire that swept through the town of Paradise and neighboring hamlets has once again laid bare one of California’s biggest vulnerabilities: With each disaster — wildfire, mudslide or earthquake — there are thousands of people who cannot find homes in a market that for years has had very little vacancy.

Over the past several days, the thousands of people who lost homes in fires at both ends of the state have scattered across California and beyond, to motels, government shelters and places like the East Avenue Church, where Patty Saunders, 89, ended up after barely escaping the mobile home community where for years she has subsisted on a $900 monthly Social Security check.

Ms. Saunders said she had hoped to go to her daughter’s house outside Los Angeles. But her daughter had been forced to evacuate her home as the Woolsey Fire, which still rages west of Los Angeles, approached. So Ms. Saunders ended up at the church.