I spent two and a half years working the night shift at, what at the time, was the largest homeless shelter in North America, with up to 1,200 "clients" per night. Most nights were quiet enough that I had plenty of opportunity to sit down and shoot the shit with the guys, and got to know a lot of them quite well.
You are correct about how people end up in shelters - in general, they're people who've been screwed hard by life.
But here's the thing:
Many of them, while they failed at fitting in with larger society, and usually had some form of mental illness or drug addiction (usually both), were, surprisingly, non criminal. They pan-handled, bottle picked, worked off the cash corners, or at worst did some "chip dealing" to cover their habits. Some even worked their way out of the pit they had dug themselves into, or had been dug into by a raw deal.
Some were petty criminals - small time dealers, shoplifters, etc. who wouldn't hurt a flea.
And some were just plain evil, fucking nasty, pieces of shit who would slit your throat for a grin.
Having a disadvantaged upbringing can make life hard, maybe inescapably hard for people.
But it is ZERO excuse for becoming a violent sociopath. I saw way too many people rise above their shitty, abusive upbringing to become decent human beings, even if they failed at life, to condone or offer any excuses for those worthless evil scumbags who used their childhood problems as an excuse for the evil they committed.
So kindly pull your fairy-tale viewing head out of your ass, get on with life, and vote conservative, mm-k? Because evil bastards don't get cured. They either get dumped in a concrete and iron hole for life, get the chair and save us the grief of wasting resources on them, or con some snivelling panty wasted "counsellor" and parole board into cutting them loose so they can go back to destroying the lives of people who work for a living and contribute to society.
Or, even better, seeing as your NIC indicates you're from Vancouver, go spend a couple weeks on urban safari down at Hastings and Main. I'll toss flowers on your grave when they pull your corpse off the street.