Asbestos definitely. I don't think I'd ever feel safe if I find someone secretly living in my house. I'd also wonder what the hell my dog had been playing at.
Asbestos gets a bad rep. As long as you don't break it apart it's perfectly safe to have in your home. It does wonders for insulation, fire prevention, it's super sturdy... You just shouldn't drill holes in it or break stuff off.
That rather depends on where you live. In my country it's been outlawed in construction since 1993. But it's still present in a lot of homes before that time.
I'll choose a man who has great skills like plumbing and landscaping and owns a foundation repair company and is happy to offer those services in exchange for living in my attic so quietly that we didn't know he was there.