Not legal advice(so Barrister doesn't jump my ass)-
If I recall correctly (which I may not), one can acquire land via acquisitive prescription based upon possession of the land for either 30 or 15 years. For 15 year prescription to attach, the neighbor needs to have a "just title" or at least title he believes to be just - i.e. he has paper that says it is his, even if it isn't, the paper is properly filed etc. This would most commonly be by mistake of a survey, bought from someone who did not have title but thought they did b/c they bought from an heir, but turns out the heir didn't have right to sell, etc.
For 30 year to attach, they just need possession of it and to maintain it. So, if they put up the fence 35 years ago, cut the grass and pay the taxes on it, it may be theirs now.
ETA - if they do not have a facially valid title or haven't had it for 30 years, tell them to move their fence.
This post was edited on 1/21 at 1:53 pm