Does society have responsibilities for some people, or not? Surely we would agree that for healthy adults society has no such responsibility and that those people are responsible for their own well-being. But what of children and those who physically or mentally disabled through no fault of their own?
My own, personal, thought on the matter is based on the idea that "the cost of freedom is self-responsibility" and that if someone in society is denied complete liberty (outside of aggressing against others) then in return society must care for them. Thus, I think it only right that those whom society denies complete liberty, minors, the mentally ill, ect., should be provided a minimum standard of care by society. Furthermore, I don't believe there is certain age where all minors turn into mature, self-responsible adults. In fact I have no doubt that there are some individuals mature earlier then 18, while many others don't mature enough to be self-responsible until years later. Therefore I suggest that society should provide for a minimum standard of care for all minors (and others who are not fit to care for themselves), and that the entry into mature adulthood should be voluntarily accepted by every individual. But, unlike how the current system of welfare is run, society should also collect the cost of the care it supplies from those who receive it, namely, their liberty. In this way everyone who accepts care from society also accepts to abide by its rules. They would be treated as minors by the state, not being given the vote, not being given the liberty to drink or smoke or do drugs, will be susceptible to curfew laws, and may required to attend mandatory schooling or employment.
Those who have voluntarily accepted adulthood in the eyes of society would be given full Liberty (limited only by the non-aggression principle) but would also be ineligible for any type of government assistance. Those who value freedom would get exactly what they want, as would those who want the government to be their responsible care taker. But, unlike as how today's system works, people would not be able to have their cake and eat it too. Today adult welfare recipients hand over the responsibility for their maintenance over to the rest of society but largely retain their freedoms to live however they want. This comes at the expense of those who want to be free and self-responsible who are forced to abide by paternalistic and moralistic laws, but also are forced to pay for the care of irresponsible smokers, drinkers, the obese, and many others besides.
The cost of freedom is always responsibility. But, today the cost of that freedom is not being born by those who exercise that freedom. This is an artificial government-created externality. I guess the cure for this gets back to our old question of how it is best fixed, by fixing the problem in the government, or by getting rid of the government altogether.