What is the statute of limitations in North Carolina regarding encroachment?

There is no statue of limiation, it actually works in reverse to that, After having had adverse possession of the property, in a open manner for more than 20 years, they may attempt to claim ownership. So they will have had to had that encroachment for over 20 years to make a claim.
And it is not automatic they have to file a suit to take possession of it.

Prior to that the legal owner may merely sue to reclaim their property

Adverse Possession laws - Information on the law about Adverse Possession - Requirements (http://law.jrank.org/pages/11865/Adverse-Possession.html)