I just saw my (large-ish US-based) bank add the following language to my account agreement:
> After your Account is closed, we may temporarily reopen your Account to resolve a dispute concerning the Account, or to accept a debit or credit to your Account, even if doing so results in your Account becoming overdrawn.
You can contact your bank (by the online chat app is best, because you have a written record) and tell them you do not wish for debits to be honored that will result in you becoming overdrawn. Many banks have a policy of honoring the debit for small amounts as a 'courtesy' to you and then charging you a fee, ostensibly to spare the customer the social embarrassment of having a transaction rejected.
Debits take place in more or less real time, so there's no reason to believe that they wouldn't be paid if you closed your account later. the bankc an just return NSF to transactions which come in after the closure.
