Whether the liver can repair itself may depend on what had initially caused the damage. For damage caused by alcohol, the liver can always repair itself if enough alcohol measures are taken. However, this may get difficult if the damage had reached cirrhosis state. If it is in the fibrosis (earlier stage) you can stop drinking and your liver will repair itself.
I had a gallstone stuck in the bile duct that connects it to the liver. My system "backed up" last December (2012), and I had "sludge" back up in my liver, and it was damaged. I just had a liver function test a week ago, and my liver has healed itself . But it really depends on the damage, and what the damage is.