And by history, I mean references, job history, etc.  

They moved out - hire a cleaning service, deduct it from their deposit, and move on.It's sad how some people live, but there really isn't much we can do about it except for screening and checking references (which you did).

Oops, sorry John Underwood meant to reference Demjan Van Der Kach on that last reply!

Any references?

If you are referring to the homeowners settling with the bank that is a very, exceedingly rare circumstance once the Sheriff's Sale date has been assigned. 

The asset protect that you are referring to is commonly solved by forming an LLC.  

Well review your landlord tenant laws for your state.. usually a month to month tenancy is only 30 day notice required prior to the 1st of the month.. written, mailed, a copy left also at front door.So your 60 day notice is very generous, I'd restate and give her another copy of that, let her know you'll provide reference.

As a current tenant, what about the company is making you stay and what about it could cause you to not refer a friend?

@Iverem RoseYou are probably referring to 475.43.

Just shoot me a PM and I can refer you to a few of them.