Unless there’s some weird law in your state, a short sale is valid at any time. The problem is that most banks take the risk that it will bring more money at auction, and it’s their call. My two cents is that whatever dollar amount your parents are willing to pay, let them buy another property in your area, avoids having them have to bid at auction and may get more bang for the buck.
See #13. I am doing a short sale purchase and I had to sign a statement that I had no financial interest, etc with the sellers.