Renters who survived Harvey across the state lost their jobs, moved into new apartments with higher rents or lived in hotels, their cars or with relatives. Some found cheaper, more far-flung residences, and at least one woman was only able to afford her apartment by keeping it virtually empty, with little to no furniture and a mattress on the floor.

Brenda Jones, whose rental home in the bayfront town of Aransas Pass was damaged during Harvey and who lived in her car for a time, had to move so far from her church that she stopped attending services there. Vanessa Wharton, a Harvey-affected renter in Corpus Christi who hears from debt collectors after she broke a lease to leave an unsafe apartment, has overdue bills and expenses, in part because she pays $100 more in rent than she did before Harvey.

Ms. Wharton’s payments on her rent-to-own refrigerator illustrate the disparities between renters and homeowners in disaster recovery, advocates for low-income tenants said. The multitude of post-Harvey assistance includes an appliance reimbursement program administered by the state and financed by the federal government — but it is only available to homeowners, not to renters.

Ms. Ortiz, Ms. Jones and Ms. Wharton are plaintiffs in the suit filed Friday.

“We do see jurisdictions where it looks very clear that homeowners are getting preferential treatment,” said Marion Mollegen McFadden , who ran a disaster-recovery grant program at HUD during the Obama administration and who is now senior vice president for public policy at the nonprofit Enterprise Community Partners.

“In some ways, it is a blind spot that the government has, except that it’s a blind spot that civil-rights advocates and others have brought a bright light to over the years in multiple recoveries.”

Rachel Zummo, a lawyer for Texas RioGrande Legal Aid, a nonprofit group that filed the lawsuit and is representing the tenants along with the law firm of Daniel & Beshara, said: “Renters just don’t have the same access to recovery resources that homeowners do. They are still struggling to recover from the setbacks the disaster caused.”