Roy Miller, a housing counselor at nearby Belair-Edison Neighborhood Inc., said most of the distressed homeowners he saw were unwilling to rent part of their houses to strangers, especially if there were children at home. Most home-sharing agencies have fewer than 100 matches at any time.

But Miss Terry did not know where else to turn. She was behind on mortgage payments, but the idea of placing an advertisement in the newspaper or online scared her — anyone might show up at her door. (In the current movie “Kit Kittredge: An American Girl,” in which a Depression family takes in boarders to save its home, a motley assortment of strangers unsettle family life.) Miss Terry turned to St. Ambrose, she said, on the advice of her supervisor, who said the agency would screen potential housemates to find a match.

Like other home-sharing agencies, St. Ambrose conducts background checks on both parties, screening out people with criminal records or histories of drug or alcohol abuse, or those who cannot afford to be stable homeowners or renters. A 10-point questionnaire sorts candidates’ feelings about pets, smoking, overnight guests and other points of compatibility.

“So far we’ve had no bodily damage,” said Annette Brennan, the program’s director (St. Ambrose provides a full range of housing services). “I say that quietly so as not to jinx it.”

In some communities, local zoning laws or homeowner associations may limit the number of nonrelated people who can live in a house. Ms. Brennan said that home-sharing could help some people caught in the housing downturn, but that its benefits were limited.

“Where we see it being of value is if someone is having short-term problems,” she said. “The average stay of a sharer is about a year, and some are much less. It’s good for someone leaving a marriage or a relationship, or going to school. You can’t count on it as a regular income. It’s a stopgap.”

After counselors from St. Ambrose interviewed Miss Terry and Ms. Ongiri, Miss Terry drove to the house where Ms. Ongiri was living alongside three men. Right away, Miss Terry said, “I’m like, she don’t need to be living here with three males. I felt as if I could help her, get her out of that area and that living arrangement. I hoped she felt the same way.”