Not a vet (unless a people-only vet counts). She ain’t gon learn shit if her brain’s starving. The brain won’t do energy-consuming things like learning and building new connections when it’s barely keeping up at not wasting away into nothingness. The brain needs a lot of energy to function! With many anorexic people-patients (because I only work with people-patients), we don’t even start psychotherapy until they put on enough weight, because it’s consistently ineffective and just leaves everyone (both therapist and patient) frustrated.

I wouldn’t call your dog untrainable until/unless she’s untrainable at a healthy weight.