Things like, "How do you feel about stretching your skills in the work force?" "What do you do when you make a mistake at work?" "How do you handle a situation where you feel out of your depth?" Etc.?

I know I would take that as a signal not to go for it if I wanted to retain stability in my life.

It does give me some ideas to consider when we extend the offer (as @Jach's sibling comment also suggests).

I've been fortunate (or not) that the hiring decisions I've played a part in have all been non-urgent with no struggle to find more candidates, so in the face of risk the org could afford to wait. The moral hazard you describe is interesting though. I don't think I would worry about it, as you say the hiring side isn't their fiduciary, and you don't necessarily know that their current situation is all that stable. I might try and assure myself that even if things don't work out, they're unlikely to be put out on the streets, since if they got past us (even with our "risky" assessment) they can probably get past someone else quickly enough, and possibly even go back to where they left depending on how stable it really was.

I'd consider being honest with them about the risk if an offer is extended. If I were on the receiving end, I'd prefer to be told before I accept something along the lines of "Honestly we're a bit unsure how well you'll adapt to our work [because of risk factors x], but we see your potential and think you'll rise to the occasion. We hope you'll come join us!" I don't think having my risk factors pointed out would affect me negatively at all, even if I think they're BS things the company shouldn't worry about, though I can see it possibly affecting the company somewhat negatively in that they're potentially giving the candidate who all-in-all they think is worth taking a chance on an extra reason to decline (and thus they'll need to continue searching which sucks). Whether that decline happens really depends on the candidate. With that information they might conclude/agree it's too risky to leave their current role for you right now, or they might actually be motivated to do better and start proving themselves right from the start especially at a company that is so forthcoming about such things. And they might fail, but at least they leave with the knowledge of what went wrong, and even if what went wrong wasn't an identified risk factor they still have your list of risk factors (some possibly valid, some BS, some that can be worked on, some that can't) that other companies might be looking out for to have for future interviews.