No, an insurance company cannot suspend or revoke a person’s driver's license for being without insurance or a lapse in insurance but the state can. If your friend believes that the insurance company somehow revoked his license then he misunderstood.
What likely occurred is that when he tried to obtain insurance is that they checked his motor vehicle record (MVR) and found that according to his state driving record that his driver's license had been revoked. If he let his last insurance policy lapse (cancel out for non payment) then in most states the insurance provider must notify the state when the lapse occurs and then the state issues penalties against that person.
Penalties for driving without insurance or having a lapse in insurance differ from state to state however they can include fines, jail time, suspension of driver's license and registration. Since the insurance company found his license not to be valid then your friend should contact your state's Department of Motor Vehicles to check on the status of his license.
If his license is revoked as the insurance company stated then the DMV should be able to advise him as to why it is and how to get it reinstated. If his license is not currently valid due to a lapse in insurance then in many states to get the driver's license reinstated he will need to file a SR-22, financial responsibility certificate. The DMV should be able to tell him for certain.