Except it is simply not true that every Westerner has safety to fall back on. There would be no homelessness crisis if this was true.

I said "pretty much". The homelessness crisis in, say, the US, affects a relatively small portion of the population; from quick looking up figures, it's less than 1% of the population.

I'm no expert on any of this, but as far as I understand it, homelessness is usually 1. transitory, and 2. usually tied to other serious issues like mental health issues, drug abuse etc. It's usually not a "lack of resources".