As in another passage you quoted, this is not native English. Ignore it for language study. Incidentally, a good English idiom is "work her fingers to the bone." The (unpleasant!) literal meaning is to work so hard that all the flesh is worn off, leaving nothing but bones. It's not a perfect substitute because it doesn't exactly carry the idea of ruining her health.

This isn't the writing of a native speaker, and is incorrect. "Work her health off" isn't a valid phrase - I imagine the writer is trying to say "Work until she becomes unwell".