[M_Grey]

It does suck, but safety on the streets is highly variable depending on your experience and what you're trying to be safe from. If your bad experiences are getting groped every night, the risk of death from exposure or someone hassling you on the streets may seem more desirable.

[rm_-rf_slash]

Daily survival is not a game theory problem. If I were homeless and expected sexual assault at shelters I would probably feel so insecure there that I would end up trying to live on the street instead, even at the risk of freezing.

It's not a rational choice but sexual assault does not often result in (or come from) rational decisions.