Am I covered by G.H.I. Blue Cross/Blue Shield if I move to Italy under an elective residency visa?
You would have to check with your provider to make sure that your plan has full coverage for you abroad. Insurers do offer plans for expats, and, if yours does not, you can try searching on 'global health insurance' for other that do. As examples:
Also returned in the Google search is this article on researching international health insurance companies.