You could say "(네) 영주권 수속(은/이) 어떻게 돼 가니/가요?" (informal) or "영주권 수속은 어떻게 돼 갑니까?" (formal). *영주권 = 영주(permanent residency) + 권(right; certificate of grant) *수속: processing (of paper work, official requirements) *돼 가다 / 돼 가고 있다: is going / progressing