Termites will leave clues to if they are doing the damage.
1. You will find dark particles in the sawdust - thems the scat of the termite. Piles of sawdust will spring up (over night usually) and you will wonder where it is coming from. The piles will be obvious, not just a few grains. In flooring issues the termites will pore a tiny hole out onto the floor and push their wastes out - leaving a pile in the middle of the room if that is where they are.
2. Termites sometimes back fill with their wastes mixed with left over wood, meaning they eat a hole through a bit of wood, then they fill up that "tunnel" and eat again. This is a mixture of sawdust and their scat. (Depends on the species) When you cut through the "wood" it no longer looks like wood with fibres and grain, instead it looks more like sand, very lightweight and crumbles (not splinters)
3. Another thing they can do is they will by-pass refilling their tunnels, instead they eat out the soft wood, leaving the hard wood behind. Tree rings are dark (hard wood) and light (soft wood) they will attack the soft wood only. In this instance you will see the rings of the wood still in place, slots or channels are completely removed. The remainder will splinter since it is still wood.
Both 2 and 3 leaves behind a structure. which in the wild would prevent a bit of wood from collapsing - in homes their is a tad bit more weight to think about.
4. You will find tiny holes (really small drill hole like holes not large holes = fractions of an inch, maybe just as big as the smallest drill bit that comes in a decent drill bit about 1/64 inch size) with piles of sawdust mixed with black scat. piling up like the sands in an hour glass.
Termite eaten wood usually looks undamaged on the exposed outer surface. Termites do not like the light, so they will eat the interior leaving a thin shell. Holes are either caused by secondary rot, or are made through dropping something or through stepping/kicking/hitting the compromised wood.
Rot on the other hand does care about the light and will eat clear through the outer surface.
4. Rot, on the other hand, can change the color of the wood. Rot takes places where water gathers, termites take place were the distance between the wood and the ground is 0 to 4 -6 inches (depending on area). Rot is often accompanied by mold, mildew and even moss - termites may, but that could be a compound issue.
Either way you should (being in North Carolina) have a termite inspection, I understand that the termites back there are as big as Volkswagens and eat buildings in a single day
(So the exaggeration goes).
Being a basement door frame we could assume water rot - however there is no "just patch" and walk away method that will really work - either if you have rot or termite damage you need to address the cause of the damage and attend to that as well as removing and replacing a bit of wood. In either case (rot or termite damage) the wood is compromised and filling with a patching compound will trap the problem inside causing it to spread through the piece of wood.
You will need to replace at least that side of the frame - when you open it up then you will know with certainty what you have behind there.
