Allow short sale owner to stay for 2 weeks after close?

[Ally Kumar]

I am purchasing a short sale property/small house. We are closing in 10 days but apparently owner didn't get notified that they have to be out soon. They are asking if they can stay for 2 weeks after close and pay me rent for that. I am not sure if that's a good idea. What if they don't leave as promised or damage the property when they leave? They would pay rent upfront at closing but should I take additional security deposit? I want to help the owners but don't want to create problems for myself like possibly having to evict them. First time buying a short sale and dealing with this situation. Pl advise. Thanks Ally