If you stop drinking alcohol does your liver get better?

The liver is able to regenerate. it depends on how damaged your liver is before you stop drinking alcohol. so in mild liver damage yes.

Liver cancer tends to occur in individuals who have stopped drinking. The typical pattern is is that an individual with alcoholic cirrhosis stops drinking for ten years or so and then develops liver cancer. It is somewhat unusual for an actively drinking alcoholic to develop liver cancer. What happens is that when the drinking is stopped, the liver cells try to heal by regenerating (reproducing). It is during this active regeneration that a cancer-producing genetic change (mutation) can occur, which explains the occurrence of liver cancer after the drinking has been stopped.