BRISTOL, R.I. — At age 82, Roberta Rabinovitz realized she had no place to go. A widow, she had lost both her daughters to cancer, after living with one and then the other, nursing them until their deaths. Then she moved in with her brother in Florida, until he also died.

And so last fall, while recovering from lung cancer, Rabinovitz ended up at her grandson's home in Burrillville, Rhode Island, where she slept on the couch and struggled to navigate the steep staircase to the shower. That wasn't sustainable, and with apartment rents out of reach, Rabinovitz joined the growing population of older Americans unsure of where to lay their heads at night.

But Rabinovitz was fortunate. She found a place to live, through what might seem like an unlikely source — a health care nonprofit, the PA

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