If your last statement said from say May 26, 2013 to June 25, 2013 then I would say no.
However if your phone is still on and operating after May 26, 2013 then you would have to pay for that advanced month.
If you pay and then cancel service you will be paying for almost a month of service for nothing.
Verizon may refund the excess days but I personally would not count on them doing so.
You have to cancel on your closing date in order not to pay for another month in advance. Not after it.
I'm saddened that you no longer want to be a member of the VZW family! May I ask why? Please update me with your specific concerns. I would love the opportunity to review your account details. At your leisure, please DM your name, wireless number and the best time to reach you. I look forward to hearing form you soon.
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If you did not cancel before the end of your last billing cycle, you have probably now been billed for your next 30 day cycle. Even if you cancel on day one of the next billing cycle, Verizon will not refund your money. You will need to pay the bill or it will go to collections. This is all spelled out clearly in the Verizon terms and conditions.
" If you cancel a line of Service, or if we cancel it for good cause, during its contract term, you'll have to pay an Early Termination Fee. If your contract term results from your purchase of an Advanced Device, your Early Termination Fee will be $350 minus $10 for each full month of your contract term that you complete. (For a complete list of Advanced Devices, check verizonwireless.com/advanceddevices.) Otherwise, your Early Termination Fee will be $175 minus $5 for each full month of your contract term that you complete. Cancellations will become effective on the last day of that month's billing cycle, and you are responsible for all charges incurred until then. Also, if you bought your wireless device from an authorized agent or third–party vendor, you should check whether they charge a separate termination fee."