It would depend upon your state's laws whether the insurance company has the right to cancel you in this manner and the method in which they must notify of the cancellation.
For example in New Jersey their insurance regulatory body states that under current regulations, companies must provide notice of payment due dates according to what type of payment is due. Renewal offers must be mailed 30 days prior to the due date.
Whether or not a policy is terminated for a late payment depends on what type of payment is due the NJ DOBI notes. Most companies will allow policyholders to make installment payments on their premiums and may even accept these payments received after the initial due date. This is permissible because a policy is already in force and there may be equity (premiums already paid) available to continue coverage for a short time. However, if no payment is received, the company will issue a notice of cancellation for nonpayment of premium. If this payment is not received before the due date, the policy will terminate.
Until the initial payment for a policy renewal is paid, there is no policy in force. Therefore, when the renewal payment is not received by the due date, the previous policy expires and the offered policy does not become effective. Should the policyholder wish to continue coverage with that company, the company would then need to write a new policy for that customer.
In NJ a cancellation notice for nonpayment of premium must be mailed at least 15 days prior to the expiration of the policy. If you do not pay your renewal premium or the premium due amount on a notice of cancellation by the date specified, the company is not required to once again tell you the coverage has lapsed, nor to offer to reinstate your policy.
While NJ insurance laws require that an insurer must be able to provide proof that a notification was mailed to the address where you have told them you reside, they are not required to mail any notice "certified" or "return receipt" and are under no obligation to ensure that these notices are received. This is true in most states.
To see what laws your state has in place regarding the cancellation of an auto insurance policy and the notification that must be given, check with your state's insurance regulator.