One night, she found herself walking the Stockton streets, her infant daughter in a carrier against her chest, pulling two suitcases full of everything she owned.

Taking shelter with a sister consumed by drug addiction, she fell into a vortex of violence. She served 11 years in prison for killing a man who she said had attacked her sister.

She emerged with a problem that confronts many people in Stockton: She was eager to work, yet she was vulnerable to criminal background checks that deny jobs to convicted felons.

She worked inside commercial freezers and as a driver. Recently, she took a job at a nonprofit that helps people released from prison set up lives on the outside.

“I’m finally living my dream,” she said.

In some quarters, the basic income experiment has provoked talk that free money will prompt people to ditch work.

“Oh, my,” said Ms. Holliman, who still carries credit card debt of more than $500 and does not earn enough money to regularly buy fresh fruit. “When you’re struggling, you’re going to rush and pay your bills.”

Stockton’s trial is meant to deliver examples of that sentiment, challenging the notion that people needing help have not tried hard enough.

“It’s about changing the narrative around who’s deserving,” the mayor said.