How often have people survived hepatocellular carcinoma?

Depends on therapy: Its really therapy dependent. Most hcc are related to cirrhosis, usually extensive and multiple and not amenable to therapy. Only early hcc can be amenable to resection and or liver transplant. Transplant is curative, as can be resection in the absence of cirrhosis.

Often: Early stage hcc is curable. There are many treatments available for hcc that have been shown to extend life. Transplant can effectively treat both the cancer and the underlying liver disease that if often associated with cancer risk.