Thanks for all the words of encouragement and advice, y'all.
To answer a few questions...
I offered to look into assistance programs for the uncle, because I honestly don't think that we can give him the kind of help that he needs. When I suggested it, the family balked. I was basically told that putting him into an assistance program is like telling him that "he's not our problem" and that we would be "throwing him away."
The other option was for FBIL and the uncle to rent an apartment together once the uncle starts a job. The agreement would be that if the uncle couldn't pay the rent/utilities, that my fiance would pay them. However, I put my foot down and said that there was no way that we would be held financially responsible for someone else's home and bills. We simply can't afford that.
The moving in option was the other alternative. Neither of the ideas are good, but this seemed like the "lesser of two evils."