I can't help thinking she was probably captive raised and released, because if she is actually entering the coop she not behaving the way a normal wild bred hen would.
They usually form small groups of 2-4 hens in the winter to find food and watch for predators. I guess she lost her group to predators or hunger. Cool that she has found your place.
Unfortunately, I think they are not well adapted to deal with chicken diseases.
I would be sure to let her...