Face is important because it came from a family oriented culture. If you were made to look bad, you'd feel even worse when the rest of your family finds out (Grandparents, relatives would talk negatively about this aka gossip). This morphed into businesses that build on relationships, the Chinese term for that is 'guanxi'.
For China, they would 'lose face' if Hong Kong became independent (or Xinjiang or Tibet for that matter).
For China, they would 'lose face' if Hong Kong became independent (or Xinjiang or Tibet for that matter).