What will happen with your insurance company if you do not turn in an accident that someone else who was at fault turned in to there policy?

As long as the other company accepts liability you don't have to notify your insurance company. Also as long as no one in your vehicle was injured you shouldn't have any problem. If you do have trouble your carrier or agent can assist you with the claim. If anyone was injured in your vehicle and depending on state law your insurance company may have to pay "med pay" claims. Med Pay is a form of coverage that usually has smaller limits and is designed to pay medical expenses no matter who is At Fault and it pays for you and your passengers up to the limit on your policy. If there were no injuries there should be no problem.