[auxym]

Given how plenty of other countries with free healthcare also have homelessness problems, I doubt these issues are related all that closely.

Have a look at the large Canadian cities: Toronto, Vancouver and Montreal. Or France, whose residents use the three letter acronym SDF to refer to the homeless.

Anecdotally, I've heard that a significant proportion of them have mental health issues for which they refuse treatment, free or not. It's also a problem of housing accessibility (interesting article: https://www.theguardian.com/housing-network/2017/mar/22/finl...) and support for transitioning to gainful employment.