No, the insurance of the car bought with the loan is normal. It doesn't matter whether you borrow it or not. If the insured eats the car, then if there is something wrong with the car, the insurance will settle the claim according to the normal procedure. Whether you have paid off the loan is another matter.

Your car, just find insurance and make a normal claim. No problem.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.