Yes Liberty Mutual Insurance does offer Accident Forgiveness on their Liberty Mutual Auto Insurance.
I have car insurance through Liberty Mutual and I have accident forgiveness on my insurance policy but luckily I haven't needed to use it yet.
I haven't gotten into an auto accident yet so haven't needed to make a claim or use the accident forgiveness but it's nice to know it's there and they offer it should I need too.
With accident forgiveness with Liberty Mutual auto insurance you don't have to worry about your auto insurance cost going up should you get into your first accident.