First, if she sells the property as a resident of FL, what are her tax implications in Georgia being that the property was left to her by the man she was seeing but never married to, and she was put on the title?

My question is as simple as the title.

At a foreclosure auction sale, though, this is a challenge, because we don't have the ability to enter the property until after the title is issued (ten days post sale).  

It's just stupid for anyone involved in the transaction to rely upon it to convey good title at a later date. 

Hopefully your name is on the deed/title.

His attorney can have him file BK, but thats about it.Otherwise buy it at auction. then you own it and get clear title.

Chances you can get a company to do title, pay cash and come to an agreement within a week is going to be very challenging.

We had one offer for $100K but that fell through due to refusal of the title company to insure title. 

Naturally your relinquished property will have to sell prior to taking title to the replacement, but this would put you in a better position for a successful exchange.

@Theresa Hansen you got me reading this based on the way you titled the post.