There is a documented 4-15% ratio of liver cancer patients who make the five-year (60 month) mark so YES there are remissions and cures out there. The actual "cure" mark is more like 3% I've been told, but hell 3 out of a 100 is still 3 people who prove it CAN happen!
I have liver cancer and have been fighting a slowly losing battle with it for 26 months. Avastin helped a little as did the folfury and folfox treatments but I started having reactions to both. Erbutux was pretty effective (actually saw a 10% or so reduction in tumor mass) but the side-effects were SO painful and terrible that we discontinued after only one treatment. Right now I'm trying the breuss diet, but since I've had a gastric bypass I can't hardly take my pain meds on it and I'm feeling very weak and tired so I may not be able to stay on it strictly enough to have any real benefit.
RFA, Targeted Radiation Therapy and surgery are the best options when they are a good fit for a 'cure' but changing your habits and diet to reduce excess sugars and all meats while limited processed foods is probably the best advice anyone can get to help fight cancer. Good luck!