It's true that the liver regenerates new cells. Some found that when 50-60% of a cancer patients’ liver is removed, it will grow back eventually. 

However, don’t take it for granted, when liver cells develop cirrhosis, a chronic liver disease in which normal liver tissue is replaced with scarred, nonfunctional tissue, it WILL NOT be able to reverse back to its original healthy status. Fatty liver is one of the most common disease causes liver fibrosis if not properly monitored, resulting in damage to liver tissue that may eventually lead to cirrhosis or even liver failure. 

“Fatty liver” includes BOTH alcoholic fatty liver and non-alcoholic fatty liver. This means that non-alcoholic drinkers or sometimes even some skinny people may also develop fatty liver. Particularly in physically inactive city dwellers with high level of bad cholesterol, consume excess sugar or harmful fats.