Most lenders require full coverage car insurance for financed vehicles. As long as you're still paying off your loan, your financed car must be equipped with full coverage (including liability, collision and comprehensive insurance) to safeguard the lender's investment.
However, the moment you've settled your loan and the car is entirely in your name, you can adjust or even drop certain coverages.
If you breach your loan agreement by opting for only liability insurance, your insurance provider might alert the financing company. In response, the lender could procure force-placed insurance, and you'll be responsible for the bill.