Wouldn’t his credit card be automatically cancelled, when he dies? Therefore the charges would be rejected automatically. If it is a joint card, cancel the card and get a new one.
We have a will and power of attourney for each other - if one of us dies, all joint accounts are automatically frozen until the probat has been dealt with, unless you have a banking power of attourney. That means even normal recurring transactions, like the mortage would be blocked, until the death paperwork has been sorted out.
Likewise, legally, all of those recurring transactions would be classed automatically terminated by the death of the card holder - here it would be more of a case of the transactions would be stopped and the widow/widower would have to deal with getting things like Netflix or Amazon Prim running again, if it was in their spouses name.