The first night that Gail Faulkner spent in her new apartment she slept in the jeans and sweater she had worn all day and never slipped inside the green-and-gray covers of her bed.

It’s an old habit. For three years, Faulkner had been stealing naps on the floor at Union Station, moving a few feet whenever a police officer woke her or the ground got too cold.

“I’m just used to being kicked out,” Faulkner said. “But no one came. ... That’s when I realized, by the grace of God, this is my place now. I can breathe.”

Faulkner’s dream — a place to live, for good — came true Monday night when she moved into Erna’s House, an apartment complex that for the first time provides permanent housing, health care and other supportive services for single women in the District who have been homeless longer than a year.

Faulkner, 56, is one of seven women who moved into the house on 11th Street NW this week in time for the official opening Thursday.

The complex is the result of a partnership between the D.C. Department of Human Services and N Street Village, which provides shelter and social services for low-income and homeless women. The 31 apartments within the complex are fully furnished, and residents can stay as long as they need housing.

Erna’s House, named for Erna Steinbruck, one of the founders of N Street Village, offers a long-term solution for the most vulnerable of D.C.’s homeless population, officials said. Homelessness has increased in the District by 9.3 percent since 2008, according to the Community Partnership for the Prevention of Homelessness.

The Human Services Department leases the building for about $750,000 a year and contracts with N Street Village to provide health and wellness services. The nonprofit projects that 70 percent of its service costs will be paid by the city and the rest through private donations to N Street Village.

“We felt we had to do this and that we were called to help here,” said Schroeder Stribling, executive director of N Street Village. “This is a group of women that can really be served by this project, by a community.”

The project dates back to 2008, when the Human Services Department decided to address a growing dynamic within the District’s homeless population: longer bouts of homelessness and increasing returns to emergency or temporary shelters in the area.

“We wanted something more sustainable,” said Fred Swan, the department’s family services administrator. “The long-stayers just kept coming back, and it was a cycle that needed to be broken.”

With that in mind, officials implemented a “housing first” model, focused on offering long-term, sustainable housing first and then treating health or social issues — a concept that has been used nationwide.

After working with other service providers in the area to tailor the program to the needs of D.C.’s chronically homeless, those who have been homeless for at least one year, the Human Services Department launched the Permanent Supportive Housing Program. Since then, the program has received almost $27 million in federal funding,which has been combined with local grants to house almost 1,200 previously homeless people in the District, Swan said.

When the program first began, most of the projects followed a scatter-site model akin to “Section 8” housing, with the District subsidizing preexisting housing on the market. But the approach has shifted in the past two years toward offering permanent housing where individuals can live in the same building.

Swan and Stribling say the model allows for a greater sense of community and is more likely to effectively address the systemic health issues that many of the chronically homeless experience.

The Human Services Department plans to open a similar housing site for single homeless men in Columbia Heights in the next two years.

“When there’s a community, there’s a sense of support you can’t get elsewhere,” Stribling said. “It’s a direction we’ve been hoping the district would move in.”

Residents at Erna’s House will have access to on-site services but will also be encouraged to go to N Street Village five blocks away for additional programming.

By Stribling’s estimate, N Street Village already serves about 60 percent of the homeless women in the District, offering a range of services, including dance classes and basic health consultation.

The partnership between N Street Village and the District offers a model for public-private collaboration during tough economic times, said Chuck Bean, president of the Nonprofit Roundtable of Greater Washington.

“We’re asking these nonprofits to get creative,” Bean said. “They have more challenges to face in this economy, but so do their clients.”

Faulkner, for example, had been homeless since 2009.

Now, in her new apartment near Mount Vernon Square, she wants to cook a steak dinner in the kitchen and eventually hang African artwork and photos of her five children, who live up and down the East Coast, on the newly painted walls. But that will come in time, when Faulkner begins working again.

The program asks residents to set aside one-third of their earned income into escrow, which they can later access if they decide to move out. For now, though, Faulkner said it is enough just to feel the weight of the keys in her pocket.

“You see these,” she said, dangling the silver apartment keys next to her face. “Nobody can take them away.”