If you're financing your car through a finance company from a car dealership then yes you must have insurance on that financed car until it is paid off.
You also must have full coverage comprehensive auto insurance on the financed car until the car is paid off in full and the title to the car is in your hand.
If you don't keep the full coverage car insurance on the financed car then the finance company will find out about it eventually because they run checks on the vehicles to make sure the person buying the car keeps the auto insurance on it.
My neighbor had a car repossessed for letting her auto insurance lapse but was able to get it back once she got auto insurance on it again and full coverage auto insurance.
The insurance is required to protect the vehicle and you must keep the insurance it on the vehicle at all times until it's no longer being financed.
You must also keep at least liability auto insurance on your vehicle as long as you own it and drive it or you can get a ticket and have your vehicle impounded by the police as well.