>you signed up for the service until you cancel it //
Maybe, that would depend on the legal terms under which you signed up. Mostly you sign up and pay for a fixed term. So contractually the expectation is that you don't continue payment.
If legally the payment is due, then that's still doesn't mean you can have authorised it on a card beyond the expiry date. Moreover you haven't authorised the payment with the new card (in the circumstances we're considering).
So the payment may be due, but it's been fraudulently acquired. There are procedures for collecting overdue amounts. Of course the companies don't want to follow those procedures and air their unfair [attempted] retention practices in court.
Hardly anyone offers a subscription service without an automatic renewal of some type. It's counter to the entire business model, which is that you spend once to acquire a customer but then earn back multiple subscription cycles from them (as the first cycle almost never pays back the cost of acquisition.)
Look at the Amazon Prime TOS, in all-caps: "UNLESS YOU NOTIFY US BEFORE A CHARGE THAT YOU WANT TO CANCEL OR DO NOT WANT TO AUTO RENEW, YOU UNDERSTAND YOUR PRIME MEMBERSHIP WILL AUTOMATICALLY CONTINUE AND YOU AUTHORIZE US (WITHOUT NOTICE TO YOU, UNLESS REQUIRED BY APPLICABLE LAW) TO COLLECT THE THEN-APPLICABLE MEMBERSHIP FEE AND ANY TAXES, USING ANY CREDIT CARD WE HAVE ON RECORD FOR YOU."
I'm guessing that their definition of "CREDIT CARD" is wide enough that they can roll the expiration date; when your card expiresd at Amazon you can just update the date without entering a "new card" - they consider the new physical card to be the same "payment method."
Maybe, that would depend on the legal terms under which you signed up. Mostly you sign up and pay for a fixed term. So contractually the expectation is that you don't continue payment.
If legally the payment is due, then that's still doesn't mean you can have authorised it on a card beyond the expiry date. Moreover you haven't authorised the payment with the new card (in the circumstances we're considering).
So the payment may be due, but it's been fraudulently acquired. There are procedures for collecting overdue amounts. Of course the companies don't want to follow those procedures and air their unfair [attempted] retention practices in court.