In a Stateless Society Who Will Care for the Lesser?

If we were to live in a libertarian society, who would take care of the orphans, elderly, sick, and poor? Would it be left to private charity, volunteers, and/or monetary support; and could the Church undertake such a role? We are confident that there are plenty of good people in society who still care about the wellbeing of others. The state is not the only guarantor of wellbeing or progress - in fact, it is highly inefficient. Charity increases with prosperity; therefore, a healthy free market could possibly cure the issue at hand.