The company then decides which one to accept for your claim. If you disagree with the decision of the company, you can appeal to them at various levels. You can also involve your state insurance commissioner's office. They may intervene for you. Finally, if you fail to get satisfaction, you can hire a lawyer and sue.
State laws vary also in regard to blame for an accident.
Usually they cannot cancel unless there are unusual circumstances. It is easier for them just to not renew your policy at the anniversary date. You may appeal such decisions to your state insurance commissioner. Usually there are laws that govern when the company can raise your rates because of bad accident or law observance history. There is one more source of information about insurance that you may turn to.