Tis...
I do not know the status. However, I do not think you can sue the State for Adverse Possession. So, if people encroached on the State RR ROW, they are probably out of luck.
Outdoorsman,
The State purchased the rail lines when the (then) current owner filed for abandonment. Then leased most of them out. If there was any "Eminent Domain" it happened back in the 1800's when the railroads were originally built. The property owners would have been duly compensated.
https://www.nh.gov/dot/org/aerorailt...ansit/rail.htm
Woodsy