Jack London, the famous homeless / hobo writer of "Call of the Wild" and "White Fang", was only able to write his first book because of the support of community libraries and random strangers who gave him a bed occasionally. Eventually, he was able to pull himself out of poverty and become one of the most famous writers ever.
If you can help those homeless people for a few years, that's all that's needed to permanently change some of their lives for the better. It will suck when the program ends, but some-help is better than none at all.
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These programs aren't supposed to be sustainable living forever-and-ever. They are parachutes to help people who are in tough times. They provide a pathway out of poverty.