“adverse possession”
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in other words, stealing...
In order to obtain title by adverse possession, they would have to live there 20 years under claim of right without the actual owner disputing their right to live there. Quite unlikely.
As you probably learned about adverse possession, this case has those elements, except the criminal invaders will not be able to have continuous possession for the statutory period (years) prescribed.
Not sure if you ended up buying that house, sounds like you had a good lawyer. As soon as a neighbor encroaches in any way on one’s land, one needs to object as that “re-sets” the continuous possession requirement “clock”. Good fences make for good neighbors is not a myth.
Yes, adverse possession is the legal term for “squatter’s rights”!
I learned of this dealing with our graveyard issues. Basically someone with a deeded property next to a closed graveyard wanted to claim it as his, since it seems “abandoned”.
Lesson is don’t ever let your property seem abandoned. Houses are very vulnerable. Visit it for a weekend reasonably often. Have someone else do the same.