If you have full coverage insurance and let a minor borrow your car will they still be covered?

If you have a minor driving your vehicle without having them listed on your insurance policy, then the insurance company will most likely deny any and all coverage if they should ever have an accident in the vehicle. You are not paying for insurance for them to drive the vehicle, so why should you expect them to pay the claim? You policy states that you agree to notify the company of all drivers and by not doing that you have committed material misrepresentation which means you broke the contract. If you broke the contract they are not liable to keep their part of the contract.