Over the last two years, Tiffani DeVincent-Clarke has shuffled through three different homes within the state shelter system. First, she lived in Salem, then Mattapan, and for the past four months, an apartment owned by a homeless services nonprofit in Cambridge.

It has not been easy going. The shelter in Salem was too far from the doctors who help DeVincent-Clarke manage her Crohn’s disease and care for her two-year-old daughter, who was born prematurely and has spent her whole life in the shelter system. At times, DeVincent-Clarke, who works as a home health aide, felt like there was no way out of her situation.

But early next month, DeVincent-Clarke and her daughter will finally have a place to call home, a sparkling two-bedroom with a balcony and modern appliances in a small building near Central Square in Cambridge, where she grew up and still has family nearby. It’s the sort of place many everyday renters would jump at the chance to lease but — with comparable units renting for at least $3,500 a month — probably couldn’t afford.

DeVincent-Clarke was able to secure the apartment with the help of a new state housing voucher reserved specifically for families who have been in the shelter system for 18 months or longer, and a new push to enlist private landlords to offer apartments to shelter residents.

“I spent a long time looking for somewhere, and now I have this place,” DeVincent-Clarke, who is 32, said with a smile.

The Rapid Housing Initiative is an experiment launched by Metro Housing Boston, a nonprofit agency that administers federal rental vouchers and other housing assistance in Greater Boston. The program aims to help shelter residents who have received one of the new housing vouchers, which cover a large portion of a resident’s rent on the private market, but are struggling to find a landlord who will accept it.

The agency has already recruited some of Greater Boston’s bigger apartment owners — WinnCompanies, Capstone Communities, and Peabody Properties — to identify units for the program, in exchange for a state incentive. And they’ve housed seven families, with 13 more in the approval process.

The effort is a nod to the fact that the state’s worsening shelter crisis is deeply intertwined with its housing crisis. Even with vouchers that can cover much of the cost, families in the shelter system often struggle to find a permanent home. Affordable housing applications are complicated, waitlists are long, and there are simply too few truly affordable apartments to go around.

The idea behind the Rapid Housing program is to broaden the pool of units that shelter residents can access. Most lack the income to compete for market-rate apartments, particularly in places like Cambridge where services are plenty, but two-bedroom apartments often fetch $3,000 a month or more — not to mention upfront costs that can equal three months of rent. Participating landlords commit to identifying apartments for shelter residents, and the vouchers cover most of the rent.

Part of the state’s pitch is that the vouchers pay a competitive rent, one that matches what they might get from another tenant. Landlords can also get a $4,000 one-time bonus for each tenant they take in with one of the vouchers, and the state is also simplifying the process of inspecting apartments typically required before leasing to a voucher tenant.

“The primary challenge that these families face is the availability of housing — we’re not building housing for families with the lowest incomes,” said Chris Norris, executive director of Metro Housing Boston. “The only options that these families have are vouchers, public housing, or the shelter system. So we’re trying to see if we can essentially compete to take some of these units off the market so they can go to the families who need them the most.”

It’s a small, rare bright spot for the Massachusetts shelter system, which has been overwhelmed by surging homelessness and an influx of migrants.

In October, the Healey administration announced a new pool of 1,200 vouchers — a mix of federal Section 8 vouchers and state-funded rental vouchers — to help get shelter residents into more permanent housing. The federal vouchers pay landlords a set amount based on geography and unit size, up to $3,060 for a two-bedroom in East Boston, for example. Both programs ask tenants to pay about 30 percent of their income.

So far, 947 of the emergency vouchers have been issued, according to the Executive Office of Housing and Livable Communities. But only 245 people have successfully used their vouchers to lease an apartment.

Why so few? Housing a family that’s currently homeless isn’t always the easiest pitch to a landlord. Some worry the tenants won’t pay their share of the rent. Why take the risk when an apartment can fetch top dollar on the open market?

Some of the landlords who’ve opened up units cite a sense of moral obligation, but even so, they acknowledge, they need enough rent to pay the bills.

“As altruistic as we all are in the world, I still have mortgages to pay and insurance and real estate taxes — we have to get market rate rent,” said Jason Korb, principal at development firm Capstone Communities, DeVincent-Clarke’s new landlord. “If we’re getting the rent through this program, why not provide a good home to someone like [DeVincent-Clarke]?”

Trevor Samios, a senior vice president at Boston-based affordable housing giant WinnCompanies, said his company is reviewing its dozens of properties in Massachusetts for units that could be set aside for the program. He hopes other landlords will do the same.

“As housing operators, this is trying to help the state through a crisis,” Samios said. “And most importantly, helping families find a home after many months of not having one.”

That includes people like Yris Ortiz. The 30-year-old has spent the last two-and-a-half years, the entirety of her son’s young life, bouncing between congregate shelters and apartments owned by shelter providers, frustrated by the affordable housing application process.

Ortiz came to the US from the Dominican Republic in 2019, and lost the room she shared when she became pregnant because her landlord did not want a child in the apartment. All she has wanted in recent years is a safe home for her son.

Next month, through the rapid housing program, she’s moving into a two-bedroom in Brookline, where that sort of apartment typically runs between $3,500 and $4,000. It’s a place where she knows she’ll have access to good schools and plenty of playgrounds for her son.

“We’re very happy; I was smiling when I heard the news,” Ortiz said through a translator. “It will just be a blessing to have our own place where we can be stable and that we can call home.”

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Yris Ortiz is an EMPath program participant.