Liability insurance is to pay for repairs on the vehicle you damaged if it is your fault. If you rear ended somebody, you are ALWAYS at fault. It doesn't matter if some idiot hit you and you hit the car in front of you because of it. So, only having liability will not cover your car. If it was the other drivers fault, and you only have liability, then their insurance would be responsible for repairing your car. BUT, if you rear end, its your fault. So you won't be covered in fixing your car.