Not likely: SF has ~7,973 homeless people now, and current spending provides housing for 14,498 "previously homeless" people: https://media.api.sf.gov/documents/Agenda_Item_9_HSH_Budget_...

Thus, cutting all budget for cash transfers could increase homelessness by 80%! (Are those 14,498 now-homeless people eligible for this year's $100k? They can't be, since you already spent it on the 7,973 currently-homeless people).

Model the situation as "X(t) people become homeless at year t, Y(t) people become housed at time t," and you'll see the most important metric is "how much can we decrease X and increase Y per dollar spent"?

"Number of dollars per current homeless" is not really meaningful at all.