Let me make clear that this is not legal advice . . . I'm working purely from memory here, and landlord tenant law varies hugely from state to state . . . So this is purely my personal and not professional opinion!
But, under the common law, in most cases, the lease should run with the land. A lease is a contract, and moreover, it is actually a form of property--leasees have rights. I believe, under the traditional rules, the new owner is obligated to either honor the lease or pay damages. I suggest your sister consult a lawyer. If she can't afford a lawyer, try legal aid. There are usually lots of people there who are very familiar with landlord-tenant law. I'd also suggest she do so right away, before it beomes a crisis situation.
I'm pretty sure that at the very least they can't just give her 24 hours notice to get out . . . I've never heard of that being legal under any circumstances, except where a tenant has repeatedly defied eviction notices.
There probably is a recourse . . .frankly, there are lots of protections for renters, but they don't know about them and thus their ignorance is exploited by landlords and banks.