All that can be meant by ‘zero balance account’ is an account with a zero balance at the end of the year. (There is no special account called ‘Zero Balance Account’).
Any account could end up with a zero balance at the end of the year.
If by ‘depository account’ you mean a deposit account (e.g. a deposit account at the bank), then yes – that could end up with a zero balance. It would simply mean that at the end of the year there was nothing left on deposit.