States' Department of Motor Vehicles (DMV) vary in how they verify insurance after a traffic violation. It is important to be properly insured though so that you are not caught without insurance. If you showed a police officer an apparently valid insurance card the DMV could still ultimately find out that you are uninsured.
In most states an insurance company has to notify the DMV if a person's insurance policy is canceled, lapsed or is not valid. When this occurs many states require you to turn in your license plates and if the insurance is not renewed or started up again your driver's license will be suspended.
Auto insurance quotes can be found here so that your vehicle will be fully insured.