On the last Thursday of August, Jennifer Livovich spent the morning simmering beans and cheese sauce in her Boulder, Colo., apartment, preparing nachos. Then friends helped her load a truck with the food, along with donations she had secured — socks, toothbrushes, cellphones — to distribute at a downtown park where dozens of chronically homeless people congregate.

“Hopefully, no drama,” she said as the truck pulled away.

Ms. Livovich has become a central figure in Boulder’s efforts to help the homeless. In 2020, she created a nonprofit, Feet Forward, to serve several hundred people whom the county estimates lack permanent shelter. And she regularly consults with, and is consulted by, policymakers, housing officials and the Boulder County district attorney. In late November she wrote an op-ed in a local paper on homelessness and substance use. To these conversations, she brings an intimate expertise: For five years, from 2012 to 2017, she lived on the streets of Boulder, often inebriated, until a brush with frostbite scared her into treatment.

“She struck a chord in Boulder that I’ve not ever seen before,” said Benita Duran, a former Boulder assistant city manager.

In 2021, the American Civil Liberties Union asked Ms. Livovich and Feet Forward to join as plaintiffs in a lawsuit that would force the city to reform its homeless policies. She was told that the lawsuit was “going to change homeless lives,” she recalled. “So of course I joined.”

Lawsuits like this one are increasingly common around the country, as cities grapple with stubbornly chronic homeless populations and a vexing legal and moral question: Can a person be given a ticket for sleeping in a public area? Or, as the A.C.L.U. contends, does such a policy constitute “cruel and unusual punishment” when there are not enough shelter beds to accommodate everyone in need?