The insurance company must notify the DMV if you cancel your liability insurance.  The DMV will then send you a letter about your insurance and you will have 10 days from the date of the DMV letter to prove that you have insurance coverage, prove that you sold the vehicle, or show other proof that insurance coverage was not required in NY.  If you do not have liability insurance, you must surrender your vehicle plates to the NYDMV immediately.  You must respond to the letter you receive from the DMV or surrender your plates to prevent the suspension of your registration and driver license.