I would. You definitely don't want to be generating notices only for the grieving family to have to deal with.
rl- where this was an application for a house loan, this would also appear to be HMDA reportable. From that perspective, I believe this application could not be deemed 'withdrawn' as HMDA instructions state the applicant must expressly withdraw the loan before a credit decision is made.
You wouldn't want to code it as a file closed for incompleteness as this would require a written notice of incompleteness to the borrower under Reg B.
It would seem this request would need to be coded as denied by the institution with the reason of credit application incomplete.