If your vehicle gets 'totaled' in an accident, and it is the only vehicle on the policy, you do not have to wait to cancel your policy. If you choose to cancel the policy, because you are not getting another vehicle to replace it on your policy, you will want it to have a cancellation date for the day after the accident. (Obviously, you want to have your policy's cancellation date to be the day after your accident, because you want coverage at the time of the accident.)
Now, if the other party's insurance company is paying you for the accident, to backdate your cancellation date to the day after your accident, your insurance company will request proof your vehicle was 'totaled' in an accident and the date the accident took place. Most insurance companies impose a ten percent surcharge to your return premium when you cancel a policy. This is called a 'short rate' cancellation. I do not know if that surcharge will apply in this instance. You will need to speak to your insurance company. Otherwise, you will be refunded any monies that is rightfully yours. Follow this link to learn more about auto insurance terms.