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.
Our lawyer didn't go into any real detail regarding the mechanics involved...he eventually gave us the OK to buy.
I had a hunch that this particular case would qualify for an adverse possession petition...but I didn't know that 20 years was the requirement.