Most insurance policies will cover any other person using your insured car with your express or implied permission to do so unless a specific exclusion applies. You should check with your company to see if any such exclusion applies such as the terms of your policy state that for listed drivers or permissive users to be covered they must have a valid license. If not, then your friend would be covered for this loss under your policy.
Your friend likely will be covered even if their license was suspended; however, other consequences may apply. The laws regarding driving with a suspended license vary from state to state but typically this offense comes with serious penalties. Also in some states if you permit a person with a suspended license to operate your vehicle you also can be cited and face penalties.
You can comparison shop your car insurance policy by getting a car insurance quote here.