If a car is uninsured and a driver is stopped by law enforcement, it will depend upon state laws usually if it is the vehicle (thus owner) or driver who gets the citation. Some states require the driver to be insured while others only require that the vehicle have insurance on it so that will help the officer determine who gets the ticket.

Some states allow the law enforcement officer to have the choice of citing either the vehicle (owner) or the driver. The driver can be given a ticket for the vehicle being without insurance since most states believe before operating a vehicle the driver should make certain it is legal to be on the road, thus having current registration and insurance.

In some cases the driver will get the ticket but will be able to get the ticket dismissed if they provide proof that the owner of the car had insurance at that time or if they will provide information on the owner. In the latter case the owner would then be sought for not having insurance on the vehicle.

Since state laws vary so much you will have to check with your state's Department of Motor Vehicles and/or Insurance Regulator to find out who can be ticketed in your state for this violation of the law and what penalties may apply.

Comment Update: A driving infraction should not affect you. The insurance typically follows the car, not the driver. If they have an accident or cause damage in your vehicle then it can impact you.