I am being foreclosed on by my mortagage company in the State of Alabama, but have the opportunity for a short sale within the next 90 days. Can squatters rigths help stop foreclosure long enough for me to sell the place?

Adverse possession laws (squatter rights) would not apply

Is there someone else who has lived on the property illegally for 15 or 20 years that may have rights under adverse possession.

The bank does not really want to foreclose, have you talked to them about the short sale, perhaps the person who wants to do the short sale can make a short sale offer ( they don't have to accept a short sale, I know several mortgage companies that will foreclose but not accept a short sale)

But get them to make the short sale but with a closing date 60 or more days out, you never know.