I had assumed that Deborah wished to exclude the right of survivorship as between the parties to the account so that each could leave by Will the share of the funds in at at death they were entitled to (which she did not specify). The bank’s mandate need not be concerned with this but the parties might surely not be happy for “either to sign” afterwards even if they are now. If they are content for a revision to “both to sign” the bank will presumably oblige. If the bank gets wind of a dispute it will freeze the account.
Whether the bank needs to recognise the death of a joint holder will depend on the mandate. If one can sign then not, absent suspicion. If the parties’ mutual trust is unaffected, and for so long as that continues, they can leave their respective shares by Will (precision as to quantum of share is desirable if only to confirm equality but especially if it is different) and leave the mandate as either to sign. Notifying the bank will be counter-productive, provoking at least its locking itself for a short time in the loo.
Many individuals put money into an account on such a basis precisely to avoid probate formalities (currently completing sometime never–"We can’t tell you now!–after the papers have been found) trusting the surviving account holder to be bound by the law of succession as regards devolution of the funds (or perhaps not, though I could not possibly comment and do not approve). The bank does not need to be notified of the death of a joint holder let alone be sent a grant. I can see as an unforeseen consequence of the Probate Service’s Meltdown as making this self-help ruse even more popular.
If the survivor alone can sign he or she can operate the account alone unless the bank stipulates for notice to it of the death. In general it will surely run the account in accordance with its mandate and avoid the intricate theology of joint ownership of bank accounts unless it is forced to interplead. Notice of an Order such as Mullenky mentions should cause it to re-consider that mandate and the effect of the Order on it. Similarly simple notice by an account holder that there is a dispute.