Wait, is part of their house actually over your property line?

That can be either a great thing, or a horrible thing for neighboring property owners, as the encroaching owner has two very opposite responses that they usually make when you tell them they have an encroachment problem: Response A is to say, "Hey, I really don't want to move my house, can I buy a 30-foot strip of land from you so I won't have any encroachment or setback problems anymore?" Response B is, "Yeah, my house has been over your property line for 10 years (that's an arbitrary number -- adverse possession statutes of limitation vary from state to state), and I knew all about it. I intended to adversely possess your property, and I am now the rightful owner of that part of your parcel." It's going to be tough, though, for them to make an adverse possession claim against your property, at least from what I've gathered in skimming through this thread, because it sounds like they have been acknowledging that it's your property and that they weren't intending to take it from you. To be successful in an adverse possession claim, you have to prove that you intended to make the property your own for the entire prescriptive period (10 years, or whatever it is for your state). Also, since you know about it now, their encroachment onto your property is no longer "adverse" -- it is now permissive, unless of course you're trying to get it back and they are actively excluding you. [These tidbits are likely 100% useless to you, but it's something I deal with for clients semi-regularly, so I figured I'd throw it out there.]

The other issue that's going to come up if their house is on your property is that it's a cloud on title -- for BOTH properties. It will be nearly impossible to sell either parcel without clearing that up.