Charity. That is already a working solution for homeless / mentally ill populations. Free market charity would also be more selective in who recieves aid; i.e. no helping those too lazy to work.
edit: a free market society would have more jobs available so the homeless popluations of people would decrease with increasing freedom. Right now government puts up massive barriers to starting your own buisness, meaning less jobs available which = more homeless. Even the most laissez faire governments restrict the economy.
I have a question for anyone who cares to answer: In my exploration of Anarchism, I have found Libretarianism/Anarcho-capitalism/Volunteerism, to be the most logical and rational approaches to a "Stateless" society. BUT, I have yet to hear anyone address the issue of the handicapped/disabled/mentally ill population... Is there a Free-market solution to caring for those who TRULY can't care for themselves? To ensure that they don't "fall between the cracks" (so to speak)? Can anyone direct me to a book, or website, which would answer this question for me?