If you have the car financed and owe money on the car and you change from full coverage insurance to just Liability insurance coverage for the financed vehicle then the finance company will be notified about the switchover to the Liability insurance and they'll know you dropped the full coverage insurance on the vehicle.
As soon as the finance company finds out you dropped full coverage insurance on the financed vehicle the finance company will send you a letter or call you and demand you put full coverage insurance back on the financed vehicle or they'll come out to your place and repossess the vehicle from you.
You have to always have and maintain full coverage car insurance on any financed vehicle you have until you have the vehicle paid off and the vehicles title in your name.
Once you have the vehicle paid off and the vehicle title is in your name you can then switch to liability insurance.