What makes a person a good candidate for a liver transplant?

Tough short answer: Failing liver basically. Multiple other factors involved including age, general health, underlying liver disease, alcohol use, hepatitis status to name a few. Best answer would come from comprehensive evaluation at a reputable transplant center.

Many factors: Good cardiovascular function, no addictions or untreated psychosis, no untreated cancers, good surgical risk assessment, and of course, the liver disease causing liver failure is amenable to treatment with liver tranplantation.