There is no grace period with auto insurance normally so if you do not pay by the given date and time on your renewal or payment plan then you policy usually cancels immediately on the date your statement notes.
If you are cancelled for non-payment of your auto insurance policy this counts as a lapse of coverage and in some states your vehicle's registration will be suspended. Also it may be difficult to obtain insurance with a cancellation for non payment with your last insurance provider showing on your credit report.
If you no longer want your car insurance coverage you can cancel before the due date of the payment or obtain coverage elsewhere but inform your previous insurer so that you will not get cancel for not paying on time.
So if you stop paying on your auto insurance policy then your coverages will stop when the time period that you have previously paid for has been reached. The cancellation notice you will receive should inform you of the date that your insurance coverages stopped being in effect.