Owner occupant wants to stay 2 months after purchase

[Daniel Paloscio]

I want to offer on a property that I've found but the owner has said that she will take offers that allow her to stay in the property for another month or two into greater consideration than offers that don't.

She's a sick elderly woman and she has a judgement for 60k pending foreclosure sale in November. She is asking 130k but I think she may take as low as 115k or 120k. Her realtor told me that she is looking with her to find a place to move into. 

The ARV on this property if I just clean it up (10-15k) is about 185k and if I rehab it (40-45k) it's about 220k. My question is should I buy this property and allow the owner to stay for a couple months, and if so how can I protect myself in the offer/contract? Could I have the title company hold 10k and give it to her once she moves out and if she doesn't within 2 months it would be refunded back to me?