A common argument against anarchists - or even just anyone who wants to abolish government-run "social security" and similar systems - is an appeal to pity toward "those who can't support themselves" - the elderly, disabled, crippled war veterans, or whoever. (I think even most liberals realize that applying this argument to children is a strawman of libertarianism because parents choose to bring their children into the world knowing the children will be incapable of fending for themselves and therefore are obligating themselves to fill the needs they created.)
I'm going to make a case that not only is this argument a laughable justification for the state even if valid and mostly invalid because of the great examples of voluntary charity in the world and the fact that poverty is in large part caused by government practices like imprisonment draining everyone's resources and market regulation harming the production of goods, but that it's actually the wrong objective.
Biological life is not inherently sacred. Now consider a hypothetical comparison: if a dead person isn't alive and a healthy and free person is, how alive is a person whose body is living but who's incapable of speaking or moving for the remainder of their existence?
Isn't that person dead? Their "life" has nothing in it for them or anyone else; it can't be enjoyable for long and there's no possibility for them to find any type of fulfillment in it.
There's only a difference of degree between that and a 90-year-old person in a nursing home who will never leave it. If your "life" is one where you're permanently unable to accomplish anything more or barely even to move, then you should accept death. A life that only exists to be kept alive is not a valuable life.
I truly believe that people who are permanently incapable of contributing or accomplishing anything should be left to die.
And before you throw a tornado of ludicrous strawmen and anger at me, no, that is not a justification for killing them. It's still murder to end such a person's life without their consent, but you aren't at all a bad person if you refuse to expend resources keeping alive someone who is only alive in the most empty sense of the word. (And forcing people to provide for this is theft.)
Secondly, I must point out that even severely disabled people in real life hardly ever fit this criterion: even people who are blind or require wheelchairs can have agency and provide value in all sorts of ways. I also believe that as human technology gets more advanced in the next few decades it'll probably become trivial to cure any such condition. But this is relevant to a few situations in real life and more relevant to hypotheticals and stories.
The main reason I'm making the argument is to counter statists who claim that if a person could be left to die for not being useful and not owning any investments in a truly market-based society, then that's unacceptable and we need some form of taxation to keep those people alive. If someone is unable to find work for so long in a free market society that they die of starvation, it's almost necessarily because they were incapable of having a fulfilling life anyway.