Honestly if what you're primarily worried about is family and kicking him out there are easy solutions that might be more work or money on your end, but enable you to say "we didn't just kick him out" without simultaneously enabling him and having him stay forever.

Example, can you afford a week in an extend stay motel for him? If you can do so offer him the choice of a month with you and a week in a motel or a month with you and then the possibility of staying longer (if he finds a job prior to the end of the month). That's extra generous and allows you to easily kick him out without a scene (by moving him first to the motel and then cutting off funding from there). It also allows you to say to family, "we told him he had a month, after that month we paid for additional time in a motel, but we just couldn't afford it anymore if he continued to refuse to look for work." That also makes it harder for him to try to claim any sort of residency since he isn't going to try to prevent being kicked out when you're paying for a motel, and after he's been at the motel for a week it'll be a lot harder for him to try to claim any rights to your place.

You could also preemptively engage with this by telling your family, "our main hesitation is that we're concerned that if we take him in and then have to kick him out it'll cause a family rift. We love you all and don't want this to impact our relationship. We're hoping it works out but we don't want anyone under any illusions or thinking that he can stay with us rent free indefinitely and we certainly do not want to have to explain to you all why we'd be having him leave. If he finds employment he can stay, we just can't afford it after a month otherwise. So in order for this to work out we'd greatly appreciate any assistance you all can give him with finding employment, money or other resources. Let's all pitch in during this month so that he has a place to go at the end of it. If anyone can help us out with the costs of housing him in the meantime please let us know."

Regardless of what he does he should be on waitlists for homeless shelters, section 8, etc. Depending on where you live and what types of housing he qualifies for these could be several months long (or with housing assistance several years). He can always get off the waitlist but if you know there is a chance he'll be homeless in a month getting him on those waitlists now makes sense, and may make the reality of his situation more clear to him. Also food stamps, etc. All of these types of programs will want him to work and some may offer assistance in finding employment. Get him connected. I'm not saying this is an alternative to employment. Since he is able to work and support himself he absolutely should be doing that, but I do think it'll make it easier to explain to your family if after you remove him from your house he is going to a shelter rather than sleeping outside. Plus, as I said before, it might make it clear to him that you mean business.