First, what does it matter if it's the customer or the executor making the claim. Your customer has died. Do you want the executor going to the media saying you wouldn't accept his/her claim and, obviously, the customer can't make the claim. If there are unauthorized transactions, who do you expect to make the claim? But to get technical, the Staff Interpretations to §1005.6(b)(5)#2 specifically state a 3rd party CAN make the claim. This isn't grey at all.
2. Notice by third party. Notice to a financial institution by a person acting on the consumer's behalf is considered valid under this section. For example, if a consumer is hospitalized and unable to report the loss or theft of an access device, notice is considered given when someone acting on the consumer's behalf notifies the bank of the loss or theft. A financial institution may require appropriate documentation from the person representing the consumer to establish that the person is acting on the consumer's behalf.
Second, if the customer was incapacitated (whether you had knowledge or not), your customer didn't make them. It could be that your customer wrote the PIN number on the back of the card (or on a piece of paper with the card) and someone took it. Either way, Reg E says the customer is not liable:
Negligence by the consumer cannot be used as the basis for imposing greater liability than is permissible under Regulation E. Thus, consumer behavior that may constitute negligence under state law, such as writing the PIN on a debit card or on a piece of paper kept with the card, does not affect the consumer's liability for unauthorized transfers. [Staff Interpretations to §1005.6(b) #2]
Last, if there were electric transactions after the customer's death, it obviously wasn't your customer. I think the executor can certainly make these claims.
The question you might want to try to resolve is did your customer give someone authorization, but that will be very difficult to prove now.