I am not sure about the debt that is actually beyond the SoL but here is a bit of info concerning the SoL of North Carolina:
a statute of limitations does not absolve one of the debt. It is an affirmative defense should one be sued.
the SoL is 3 years so at least some of the debt would still be within the SoL.
if there were any payments on any of the debts, the SoL was reset to begin on that date
so, before I would get to set on claiming the debts are no longer collectible, I would determine just which debts would be within the SoL and plan on paying them.
as to the others, I suppose you could claim they are beyond the SoL and see what happens. The worst that could happen is the estate would get sued and if the SoL is an acceptable argument, any debts outside of the SoL would not be collectable through the courts. If found to be valid, pay them.
hang on for some others input.

