Its function can change over the decades. A rental that generates income for young homeowners might later become a refuge for returning young adults, then become a way for older homeowners to defray housing costs and remain in their neighborhoods.

In an aging nation, an A.D.U. makes particular sense for people in their 60s and up who don’t want to move and will need nearby caregivers, either family members or hired aides. Mr. Silva died at home of pulmonary fibrosis, and in his final weeks and months, his daughter and son-in-law had to walk only a few yards to help care for him.

“They came over and did whatever needed to be done,” Ms. da Silva said. With such proximity, “everybody has to be respectful,” she acknowledged. “But for us, it’s been wonderful.”

As affordable housing grows increasingly scarce for both young and old, A.D.U.s provide several advantages. “They create housing that doesn’t alter the look or feel of a community,” said Zoe Baldwin, the New Jersey director of the Regional Plan Association, a nonprofit group in the Northeast.

“It’s a way to add capacity within the existing footprint,” she said, a strategy planners sometimes call “gentle density.” A.D.U.s don’t require much government investment in infrastructure, and they reduce energy consumption and costs.

Accordingly, they are growing more popular. Ten states and the District of Columbia, as well as many municipalities, have adopted or revised laws to encourage A.D.U. construction, reducing barriers like zoning, parking restrictions and onerous approval processes.

In California, which has passed a series of laws enabling the use of A.D.U.s, permits rose to nearly 20,000 in 2021 from about 1,200 in 2016, the year before the first law took effect, the state has reported.