Only a difficult problem against a background of having to pander to delusions.
Those less able to take care of themselves favour the politics of irresponsibility and parasitism.
Those with serious brain problems prioritize, above all else, being seen to be responsible. They don't want your "pity" by which they mean they want the handouts to be mandatory, not something they have to ask for as a favour. They prefer to enter a life-and-death struggle rather than risk being socially expected to show gratitude. Only when actually landed on death's doorstep do they realize they aren't willing to sacrifice everything, revealing everything they do up to that point is bluffing and bluster. Crazies be crazy.
As a bonus, the mentally deranged are aware they're plus ungood in the thinker, and envy those who aren't. The politics of irresponsibility promise to allow them to carry out their jealous fantasies, going full Harrison Bergeron and punishing the healthy for being healthy.
As always, they cannot punish anyone who is really all that healthy. The healthy will resist, and have this thing called competence which makes it work most of the time. However, the crazies can be scammed into thinking otherwise. At best the crazies can employ the upper lords to punish the burghermeisters...should they manage to bring anything to the table that upper lords have demand for.
Women often feel entitled to be taken care of, and modern society flatters this narcissism. It wouldn't matter much if birth control didn't exist, because they would get pregnant anyway and end up taking care of the kids, thus at least partially earning their keep.
Madness is only feminine in the sense that they can't pay for themselves and have to be coddled like a child unless you're okay with letting them starve to death.