Buyer should've automatically been sent a replacement card with a new future date; it's a concern if it should've been received by now but not been received, in case it's been stolen en route. Old card should automatically not have been accepted, though payment providers can make mistakes, so for peace of mind it'd be a good idea if the buyer contact their payment provider about this and ask if, ideally, they can be sent a new card with a different number not just a new future date.
Of course I hope in this case there's nothing untoward (or not too untoward). As someone who a year or so ago had their card hacked and £Ks stolen, you can't be too careful keeping an eye on statements and things like expiry dates, and on the providers themselves! Using an out-of-date card is understandable, it's human nature to make mistakes, but maybe now consider putting the expiry date of your card(s) into your diary so you can deal with any problems in future in a timely way, and not rely solely on your card provider.
I once, at short notice, chased a provider to send the renewal card as I was about to go on holiday, needed to receive it and would be using it; I was told they'd sent it weeks ago, they stopped it, sent a new one, got it within days. I now diarise expiry dates, and in advance as some merchants won't accept a card with less than a certain amount of time left on the card e.g. hotels (understandably where the stay is close to, on or after expiry date) and ?airlines.
If you don't receive the renewal card in time, I definitely advise checking with your provider in case it's been stolen en route (not just a mistake by them) as with theft/hack a number of bad transactions inevitably go through before they can warn you of "unusual activity", and/or they wait until your spending limit is near before they warn you.
