Have to buy in full by end of day with 10% deposit right then and there. 

Put it in writing and let them knowing they are out by Jan 15 and leave the apt in good condition with no trash, and pay $xx (say 50% of what’s owed) you’ll return their security deposit and not do anything with eviction or collections.

Well.... if you liked her you can ask for a bigger deposit, or get a co signer etc. 

Some are living check to check and in reality need their deposit back to make adeposit on the new place, which puts them in a bind.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

Get deposits and last months rents on closing.

It sounds like they charge a tenant whatever fee they can get and that is not a pet deposit in your favor. 

I'll open a local bank account and have them all deposit their rent automatically or pay online.

Then you just bought a whole lot of trouble with your assignee.You might be able to limit your liability to your deposit, but that's an obligation.

Only been sued for return of security deposit and never lost.