A coma togther with liver failure is going to be very serious. Usually the liver has a good ability to repair itself however if there is years of alcohol abuse and the liver is now cirrosed then the ability to repair itself is no longer present because the liver is now full of scar tissue. When the liver does not work then toxins build up which contribute to the coma and also cause other problems such as with the kidney.
The only solution for the liver damage would be a transplant and that is not something that is easy to arrange.
If the liver is not irreversibly damaged then there is some hope that time might help matters. You would need to discuss the situation with the patient's doctor who will have all the information to hand.