Like many older Americans, Shazzi Felstein recently found herself in an unexpected financial bind. About a year ago, she noticed that her savings had dwindled. To her horror, she realized that her monthly Social Security check would not cover her rent-stabilized one-bedroom apartment in Chelsea and monthly expenses like utilities and food for much longer.

A former computer systems analyst, Ms. Felstein, 73, had always saved as much as she could and had enjoyed relatively stable finances. That changed in 2011, she said, when she lost about $80,000 in retirement savings after investing in a company that turned out to be guilty of fraud.

The owners of the Massachusetts-based Inofin Inc., a subprime auto loan company, swindled hundreds of investors, and the company entered into involuntary bankruptcy. Ms. Felstein has been unable to recoup her money, although the company’s founders pleaded guilty to fraud and were sentenced to jail.

“I felt very lost,” said Ms. Felstein, a former nationally ranked table tennis and Scrabble champion. “I have always paid my rent on time, and I knew if I didn’t do something, I wouldn’t be able to live here anymore.”So she did what many others do to keep costs down in an expensive city: She found a roommate.

Instead of placing an ad online, however, Ms. Felstein turned to the New York Foundation for Senior Citizens, a Manhattan-based nonprofit. The group has been operating a home-sharing service since 1981, matching people who have space in their homes with those in need of affordable housing. It is one of a number of similar programs that have emerged across the country as the population of older Americans grows, as a way to help people stay in their homes.

The concept of pairing older people with younger ones, particularly those who are not family members, is not a new one: It was popularized by Maggie Khun, an elder-rights activist who opened up her Philadelphia home to others for more than 20 years before she died in 1995. Today’s home sharing, however, is as likely to be between those of the same age as it is to be intergenerational. The crucial thing is that it involves two or more people sharing an apartment or a house to their mutual benefit. And finances often play a big role.

For those who are still working age, it’s getting harder to pay the rent: According to a StreetEasy survey, rents in the city rose twice as fast as wages between 2010 and 2017. The lowest rents (those up to $2,300) rose 4.9 percent annually since 2010, which means someone who paid $1,500 a month in 2010 likely paid nearly $600 more for the same place in 2017.

For baby boomers entering retirement, financial security is also increasingly hard to come by. Many Americans may think they have plenty of savings, but about half have not saved enough to maintain their pre-retirement living standards, according to a recent estimate by the Center for Retirement Research at Boston College. The rising cost of health care, increased life expectancy and lower interest rates only exacerbate the situation. In addition, a Fannie Mae survey found that baby boomers are more likely to be carrying mortgage debt into their retirement years than previous generations were.

To Ms. Felstein, who was confronting these realities, there didn’t seem to be any other option than taking in a roommate. The New York Foundation for Senior Citizens connected her with a licensed social worker who asked a host of questions, including details about her sleeping habits, personality, interests and daily schedule. She also had to provide three personal recommendations and her rental agreement, to prove she was on the lease.

And she was asked to describe what she considered the ideal roommate. Her response: someone who wasn’t home much.

“I knew it would be a long shot,” she said, “but I thought I should be honest.”

She found her match in Yukari Honda, a 27-year-old graduate student in interior design at the New School. Ms. Honda, who is from Tokyo, is often at school from morning until past midnight.

A year ago, Ms. Felstein moved out of her old bedroom to make room for Ms. Honda. She replaced the living room sofa with a bed, turning the living room into a bedroom for herself. Fortunately, there is a separate kitchen and common room where Ms. Honda studies and Ms. Felstein keeps reams of fabric for her quilting.

The two split the utilities and the $1,145 rent equally. They rarely share meals or do things together, but have found that they seek each other out in other ways. “Shazzi is so patient, she has helped me for hours with my schoolwork,” Ms. Honda said.

Ms. Felstein, an avid quilter, said she has been thrilled to talk about design and assist Ms. Honda with her assignments. In return, Ms. Honda has been helping out more with the housework.

“Getting a roommate at my age certainly required some mental adjustment,” Ms. Felstein said. “But it has been wonderful in so many ways.”

Susan Bendes, the shared housing coordinator at the Women’s Rights Information Center, in Englewood, N.J., said the nonprofit, which has found affordable housing for Bergen County residents since the 1970s, believes there is an urgent need for public policymakers to promote home sharing to seniors to prevent homelessness.

“I have seniors who call and ask me all kinds of questions because they’re in dire need of financial assistance to stay in their homes, but they tend to be gun-shy when it’s time to actually bring in a tenant,” Ms. Bendes said. “There needs to be more dialogue on how and why home sharing should be a normal thing in our society.”

Statistics show that the number of older Americans who are homeless is growing. In 2007, homeless people 62 and older who sought shelter accounted for 2.9 percent of the country’s homeless population. By 2016, the percentage had risen to 4.7, according to estimates from the National Alliance to End Homelessness, a Washington, D.C., advocacy group.

“People were doing O.K. until the recession,” said Nan Roman, president of the alliance. “But as people lost their jobs and struggled to get rehired, some lost their assets over time.”

Wendi Burkhardt, chief executive of Silvernest, an online home-sharing and roommate-matching service geared toward older adults, thinks that society’s penchant for independent living has clouded the conversation about how we age.

“I really think the ‘Golden Girls’ were early trendsetters,” she said, referring to the popular TV sitcom from the late ’80s and early ’90s, in which four older women lived under the same roof in Miami. “Why wouldn’t you want to share your home with others, whether it’s for financial reasons or for companionship?”

Although placing an ad and setting up a profile is free, Silvernest charges those who have rooms to rent about $30 to use the messaging service to communicate with potential roommates. Those seeking rooms pay the same amount, which covers a background check and gives them access to the listings.

More than 70 percent of those who have placed an ad since the company was started in 2015 were motivated by financial reasons, Ms. Burkhardt said, noting that while most of the company’s clients are in the West, the service is available nationally.

The real estate listings site Trulia estimates that there are 3.6 million unoccupied rooms that can be rented out in the country’s largest housing markets — and there may be more than 17,700 spare rooms that can be rented out for about $868 a month in the New York area alone.

Sarah Oswald, a relationship coach who lives in Boulder, Colo., said she messaged numerous people through Silvernest to find her father, John Oswald, a roommate.

Mr. Oswald, 69, lives in a one-bedroom rent-stabilized apartment in the West Village and has no pension to rely on, he said, because he worked in the nonprofit world for years. Health issues stemming from his service in the Vietnam War also took a toll on his finances, because numerous surgeries on his legs prevented him from working at times.

Ms. Oswald said she tried using Craigslist and university housing boards, but they were difficult to navigate from afar. With Silvernest, she said, she was able to carefully read all the profiles, which made choosing whom to message and to introduce to her father much simpler. “The vetting the firm does for you helps,” she said.

Other start-ups are following suit. Nesterly, an online portal that matches intergenerational roommates, will start offering services in New York this year after being introduced in Boston last fall. “We’d like to help create new units of affordable housing at a time when there’s a dire need for it,” said Noelle Marcus, a founder.

Elizabeth Rosania, 86, learned a painful lesson when she found boarders through the classifieds in the local paper. After her husband passed away in 2013, a year of living alone in her four-bedroom, three-bathroom house on a four-acre estate in Lebanon, N.J., left Ms. Rosania lonely and seeking company.

She had worked as a nurse her entire life, she said, and she wanted to continue helping people in another capacity. Her first few tenants, however, were too much for her to handle. One female tenant in her seventies was addicted to OxyContin. Another tenant, a struggling alcoholic in her fifties, stole a nine-foot satellite dish, jewelry and appliances, Ms. Rosania said.

But last year, she found John Costanzo, 61, with help from social workers at HomeSharing Inc., a nonprofit in Bridgewater, N.J., and the two became fast friends. They now watch TV, run errands and eat most meals together.

For Mr. Costanzo, a former Marine who owned a crane-rigging business and is on disability after several back surgeries, affordable housing was essential. He pays $600 for his room, a monthly fee that includes utilities and cable. He is not allowed overnight guests, alcohol and drugs are prohibited in the house, and he must keep the bathroom clean at all times.

“I think my blood pressure is lower and I’ve lost 43 pounds since I moved in,” he said.

“I wouldn’t know where,” Ms. Rosania shot back with a smile.

Home sharing, of course, is not just for those who need the money. Taking in a tenant for little or no rent in exchange for household work suits many who have extra space, like Thelma Chesney, a Brooklyn Heights resident.

Ms. Chesney, 91, started living with a new roommate last month. In exchange for light household work — taking out the garbage, cleaning the house, shopping — Grace Linderholm, 23, an artist who recently graduated from New York University, gets to live on the top floor of Ms. Chesney’s house for free.

A former associate professor at the New York University Silver School of Social Work, Ms. Chesney said the four-story brownstone became “a lot of room for one person” after her three children moved out and her husband passed away in 2008. She finds all her lodgers through word of mouth, and also rents out the ground floor at a reduced rate, in exchange for handyman work done on the brownstone.

But more important than the work her tenants do, she said, is having her home lived in, especially when she is on vacation or visiting her children. She recalled previous boarders, including one who practiced the cello for hours on end and another who helped her sew buttons on her clothing.

“I’ve been able to coexist with everyone quite well,” she said. “Having someone fetch you milk in bad weather is quite convenient.”

Melissa McHam Green, a licensed social worker and eldercare manager in Brooklyn, has helped some of her clients find roommates and agree on mutually beneficial guidelines. She advises those interested in home sharing not to go about it on their own: Go through a nonprofit service, she said, or ask a trusted eldercare professional, friends or family to help properly vet the prospective roommates. And before you sign a lease with a boarder, make sure to do a background check.

“You need a huge amount of trust and to be very clear with your expectations,” she said.

“But if you have the help you need to stay in your home — and the tenant gains affordable housing in exchange — I think there’s much to gain socially and spiritually when young and old live together.”