As I understand it, the case for the welfare state is the sense that “negative” liberty (being free from the coercive interference of others) is not an adequate condition for achieving a successful, flourishing life. Rather, “positive” liberty — the notion that liberty has its genuine virtue to the extent that one possess the power to direct his or her own life — is akin to having autonomy (or control) over one’s life. The role of government charity, according to the advocates of a welfare state, is to provide a baseline standard of living so that people have greater flexibility in pursuing their interests.
I have my own concerns that charity, particularly government charity, acts more as a snare than a genuine safety net; that concern aside, I think libertarians can agree with left-liberals that positive liberty (or autonomy) is valuable and something to cherish. And liberals are right that negative liberty is not a sufficient condition for leading a meaningful life, but they are mistaken in not recognizing that both negative and positive liberty — complete liberty — are necessary conditions for human flourishing.
As a matter of practice in promoting liberty, someone who sees little benefit from their negative liberty in overcoming their struggles is going to have less regard for that liberty and be more willing to surrender it or interfere with the liberty of others. Again as a matter of practice, to someone who comprehends the nature of coercion, it does not follow that the state’s coercive tools are the least bit adequate in building positive liberty. That understanding comes from the fact that coercion is a tool of destruction.
Granted, when used properly, coercion can be used to destroy coercion and thus defend negative liberty. Defensive coercion acts as a counter-interventionist measure that indirectly aids progress by ensuring that voluntary exchange can take place. But any progress is still contingent on people being free to think and to act on their best judgements, an objective requirement of which would be to bar coercion from social interaction. That is the essence of negative liberty, a precondition for positive liberty to exist.
With that said, it is possible for the state to provide a semblance of a social safety net, but only by confiscating greater amounts of resources to overcome its own destructive nature in such a way that undermines its continued prospects. So along with an ever-shrinking source for revenues, government charity is inhospitable to autonomy, since welfare recipients shift their reliance to the good nature (or long-term parasitism) of program administrators, who are the primary beneficiaries of the welfare state.
A social safety net respecting negative liberty and which provides genuine autonomy is mutual aid, not charity and particularly not charity tied to career bureaucrats or the election results of politicians and their political appointees.