Common sense actually should be telling you that you need to continue to make payments on your vehicle's loan or lease, though it has been found a total loss by the insurance company, until the actual insurance settlement has gone through and your lien holder is paid off. Your lien holder has no guarantee that they will receive all of their money until they actually have a check from the insurer to apply to your loan and pay it off.
Until the balance of your loan or lease is paid by the insurance company paying the actual cash value (ACV) of the vehicle you are still responsible to make your monthly payments. Your finance paperwork probably states this someplace. Your finance company will hold you responsible to keep with the terms of your finance agreement which includes you making your monthly car payments until the car is paid off.
Until the ACV is paid to the lien holder they really do not have a guarantee that they will receive the money since your claim could be denied or delayed, etc and your payment is due still. And if the value of your vehicle is less than what you owe, then even after ACV is paid to your lien holder you will owe them money so keeping up with your payments will help lower that amount and not get you behind.
You should read through your finance agreement and see if it specifically mentions what happens in a total loss situation, if it does than likely it states that you will need to continue making your normal monthly payments until the car is completely paid off by insurance companies or by you. This is how a financial institution protects itself from a person from totaling out a vehicle and walking away without paying back the monies they were loaned to purchase the vehicle.
You may also be wondering about if you must keep your insurance on your totaled out vehicle. The answer is also yes, at least for a while. Most insurance companies advise that you should not remove a total loss vehicle from your insurance policy until you are no longer using a rental vehicle and your damaged vehicle is no longer registered in your name. The vehicle is usually no longer is your name at the end of the insurance settlement process when you sign over the title to the insurance company and receive your check for the actual cash value (ACV) of the vehicle.
In many states, an insurance company will be able to remove the vehicle from your policy retroactive to the accident date when you are ready to take it off of your policy. You should discuss with your insurance provider at what point they would advise you to remove your coverages from the totaled vehicle and if they can make the cancellation retroactive or not.
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