No, but people are mobile, and the houseless are also people who communicate through the internet and share where assistance is available.
If free, safe lodging is available without restrictions, demand will quickly outstrip supply with folks moving from other cities (LA, Seattle, Portland, etc) to fill the available rooms. It's a $50 bus ticket, city officials will likely fund these tickets for them to get to SF to take advantage of this. SF had programs for this exact thing to get homeless out of SF [1]
Which means every city should do this to reduce their homeless population. The "don't do it because homeless people will move from elsewhere to get this benefit" is a race to the bottom.
Housing homeless people reduces overall homelessness. If we do it enough, everyone will be housed. Part of this is lowering housing prices, another part of this is housing people who can't house themselves (for various reasons).
If free, safe lodging is available without restrictions, demand will quickly outstrip supply with folks moving from other cities (LA, Seattle, Portland, etc) to fill the available rooms. It's a $50 bus ticket, city officials will likely fund these tickets for them to get to SF to take advantage of this. SF had programs for this exact thing to get homeless out of SF [1]
1 - https://www.vice.com/en/article/bvg7ba/instead-of-helping-ho...