The State of North Carolina does have free primitive camping in some state parks, but you can not make a permanent residence on the property.
Free primitive camping spots in North Carolina are located in the Croatan National Forest, Uwharrie, and in Western North Carolina.
If you did want to find a place to go live in the woods, you would need to go to a town near the Nanatahala State Forest. In fact, there are probably people living in these woods, but I’m not sure you would want to run into them.
Here is a map of free campgrounds in North Carolina.
You can read more about camping in North Carolina here.