My brother teeters on homelessness all the time. Thanks to a brief stint in the service the VA has kept him off the streets (he was given a medical discharge due to his alcoholism 40 years ago, but that's still considered an "honorable" discharge, which drives my husband, who served 2 years in the Marines in the 70s, absolutely crazy).
He had burned ALL of his bridges with the VA, and I researched homeless shelters in his area. There was one run by Catholic Charities which had an enclosed, fenced in lot with tents (it's in Florida, so no cold-weather issues). He was just about to do the intake for that place when he wound up back in the VA for a medical issue (detox), and the day he thought he would be discharged back onto the streets, a VA social worker offered him a 28-day program again. She told him: "Our mission is to get every homeless veteran off the streets."
So as the sister of a person with multiple chronic psychological issues, it is truly a difficult dilemma. When I interviewed Indian psychiatrists for a market research project he said there are are no homeless in India because the families and communities take them in. They consider it their duty. But there's no way I would invite my brother to live with me, and I consider myself a bleeding heart. We did it once, and it was not easy. My DH literally picked him up physically and threw him out after a week, because of his drunken behavior, his arrogance, and his insults (talk about biting that hand that feeds you).