Adverse possession laws say if you build a fence or upkeep the grounds for a certain amount of years and they dont utilize it the grounds become yours. Just take it they arent using it and is an inefficieny allocatipn of resources
Assuming he is in Louisiana, that is 30 years. Then you have to petition to quite title, which means you are probably dropping 3k+ on an attorney if there is no one to dispute the the claim.
Context clues say they offered to sell for $2k. If I was him, I'd just offer a firm $1k and be done with it. Russian has the right idea here.