Can You Cancel Car Insurance With An Open Claim? 
To the best of my knowledge an open claim does not obligate you to remain with your current carrier . I personnally would not recommend cancelling coverage withthe carrier that you are with as you already have a history with them and will more than likely be receiving a lessor rate than with another carrier . Cancelling your coverage will not remove you from any liability that arises from the claim that is not covered by your insurance carrier . If you are concerned that a claim is not be handled properly contact your agent and let them know so that they can attempt to help you find a resolution . 