Nothing has ever tried to dig under our run, but we've had woodchucks dig under our big pole shed twice and the garden shed coop. Pain in the... Cute faces, but a pain, when they dig under buildings. One even dug down next to the house foundation one year. This is over 25 years, so guess it's not that bad. Still annoying, though!
Yours could be any of the predators mentioned, too. Reaching through an opening to get a bird sounds like a raccoon. They've reached through wire fencing to dismember birds, when the openings were large enough to get their little arm through. I cover all openings to the coop with 1/2" hardware cloth.
You could put out a live trap and see what you get. To prevent digging, you could also stake down wire on top of the ground, around the coop, instead of digging it in.

Yours could be any of the predators mentioned, too. Reaching through an opening to get a bird sounds like a raccoon. They've reached through wire fencing to dismember birds, when the openings were large enough to get their little arm through. I cover all openings to the coop with 1/2" hardware cloth.
You could put out a live trap and see what you get. To prevent digging, you could also stake down wire on top of the ground, around the coop, instead of digging it in.