this is less of a dichotomy than i think is described here, though: almost all people in the second category were at one point people in the first and end up there because the support described in the first category disappears. when you become homeless, that frequently means you lose almost everything–and it’s really, really hard to build up from nothing in modern society because the expectation is that you have money to survive, and there’s only so far people are willing to pay your way forward.
(there’s also the reality that even if you have something, there’s only so long you can make that last without a job–and for a homeless person getting one can be functionally impossible, no matter how menial. housing is also catastrophically expensive, so even if they clear the job hurdle once they’re down, the housing one may be likewise impossible to clear. this treadmill is a big part of why so many people become visibly and persistently homeless)
As someone who deals with homeless and near homeless a lot you’re absolutely right. Our system constantly fails the most vulnerable by not providing then with support when they have none. I do my best to provide them with contacts to resources and social workers but those resources are incredibly limited and I’m sure most end up without help regardless.