This is a very good question. I want to move and continue renting, and have been tempted to ask landlords a few questions about the purchase history but have thought better of it. I noticed in the New York Times an article that said a landlord (bank) can evict tenants within days, but that new legislation is to give tenants more protection. I believe the banks would have to continue renting to the incumbent tenant for up to six months, after a bank takes possession. If you don’t have a realtor (and I don’t) I can’t think what you can do to protect yourself against this kind of thing.