Permanent residency for a former Chinese citizen.

My friend has got to stay in China with her family for 12 months due to having emergency surgery. She will need further surgery there. She has only just given up her Chinese passport. She has a very large supportive Chinese family. She also has a 6 year old daughter.
So my question is could she obtain permanent residency for herself and her daughter? Could she obtain permanent residency on medical grounds?
Thank you.
George.