Just going through this one myself.
Device plan will end without issue.
Airtime - make sure you have a copy of your invoices and payments before the contract expires. All my information dispappeared on the day that the contract ended on Dec 14th. Despite me giving thirty days advance notice for ending the two year contract on the day it finished, I was still charged another months airtime, but could not check it as the account had disappeared. I still have a login as I also have an old O2 PAYG emergency brick.
O2 assured me I would get a corresponding bill at the end of December with a refund. I did get a bill but it simply told me I had nothing to pay, but no mention of refund.
More time Contacting O2 again on New Year's Day and was told the refund had been placed on my account!!! one small problem here, as you know, I had no access to the account. A refund to my bank account is now being processed but it could take ten working days (three weeks!!!) to come through. It takes seconds to go in the opposite direction!!
Hope this helps you be aware of what may happen and to be ready. Very poor!!