As uptown said, providing valid credit card information creates an authorisation for a merchant to charge to you, if your card expires after that authorisation has already been created you can still be charged and that charge will still be approved by your credit card provider. This is a common problem for people who take out short term loans and then think they can cancel their card to escape being emptied out when due day comes.

Cancelling a card (or letting it expire) prevents new authorisations, it does not cancel previous authorisations.

Also there are automated credit card update services, so if you get a card reissued then vendors can get their card on record updated.

Better double-check. Sometimes credit card companies allow charges to continue to flow through old, expired, even cancelled / compromised credit cards. I learned first-hand that a card can still process charges after AMEX allowed about 7 months of Netflix charges to continue to be processed from a card number I'd reported compromised.

What may be happening there is that Netflix is connected to services provided by the card companies to stop interruptions to recurring billing for reasons like this. Long story short if Netflix receives an error code from the payment gateway that says something like "Card expired/Card changed" it'll make a call out to this service with the old card data. That'll do a look up and return the new data to Netflix who then updates their records and charges away happily.

My bank hit me with a fee when Dreamhost charged an expired card ... It was my fault for not keeping my account up-to-date but it does seem like the kind of thing their billing code could check.