Soon her car broke down, forcing her to rely on family and the public bus to get to work, which did not always happen.

Her boss had been kind, but patience wore thin.

“She was like, ‘Your baby sitter bailed on you, your car broke down. What do you have left?’ ” Ms. Wallace said. “She said, ‘If you can’t get something worked out, I’m going to have to let you go.’ ”

Even after she lost that job, Ms. Wallace remained confident she could find another.

Then it dawned on her. Given the state of the social safety net, unemployment might provide the solution. She could qualify for cash assistance, which would require her to enroll in a state jobs program and would include help securing child care.

“It’s something I have to do to get where I need to go,” she said.

She plans to stay on cash assistance long enough to gain child care, then find another job. She would then lose cash assistance, but could hang onto child care as long as her income stayed below the eligibility limit.

These were her thoughts as she stood in an airless office, amid the sounds of unhappy children in the arms of tired women, waiting to hand in the forms to receive welfare.

“Oh no,” she said, peeking inside a white envelope full of documents and spotting a brown smudge. “My kid got chocolate on her birth certificate.”

She ducked into the ladies room and dabbed the stain with wet paper towel.

When she stepped outside an hour later, beneath a pounding Arizona sun, $220 a month was headed her way. Her daughter was waiting at her parents’ house. Her future — a working car, a steady job — was waiting out there, too, she told herself, though it had a way of coming in and out of focus.

“I’m just trying to get my life situated to where I can look beyond the day to day,” she said. “I hope it all falls together the way it all fell apart.”