Whenever you finance a car with a loan the finance company will require you to have full coverage car insurance until the car loan is paid off.
That goes for used cars and new cars whenever you have the vehicle financed the finance company wants the vehicle fully insured to cover the loss of the vehicle in the event of damage to the vehicle by weather or damage to the vehicle from a wreck.
If you drop the full coverage before paying off the financed car then the finance company will repossess the vehicle so always keep full coverage on the vehicle until the car loan is paid off.