If a Hungarian citizen works abroad, the Hungarian health insurance must be informed within 15 days, and his insurance ID will be cancelled. Since he is insured abroad, he is entitled to use the health care system there. He should not pay any health contribution in Hungary, and he can use the Hungarian health care system only with an EU insurance card for the medically necessary degree, just like a foreigner.
Warning: If he uses the Hungarian health care system more than necessary without valid employment and insurance in Hungary, the costs of the treatments must be paid personally!