"...they all wish their AS could find a partner and a job which pays enough to lead to an independent existence."
IMO, they need to let go of the wish that their AS "could find a partner" or, at least, put it on the back burner. The idea that he "needs" a partner in order to move out may be part of the problem. I think it gets back to the assumption that women can cook, clean, etc. for themselves, but men... ahh, poor men... they need someone to do all that for them. (I'm glad they're not saying specifically, "wife" or "girlfriend").
Oh, I understand their wanting their AS to have romantic love in their lives, etc. But, IMO, the only thing that impacts the parents' lives is if AS is financially independent and has moved out. IMO, that's what they need to focus on, if anything.
Iv heard that some people won't go with someone who is still living w/ their parents. So they might not find that partner until they become independent.
Regardless, if an AC is paying their way as best they can and doing their share of household chores, etc., and all are happy w/ the situation, then fine. But if the parents want their AC out and/or financially independent, they may have to sit down w/ them and set some (realistic, of course) goals, some kind of deadline for finding a job and a flat of their own.... Just my thoughts...