Clearing a balance in undeposited funds

If the 'undeposited' account is carrying a net balance, it is not due to a 'zero entry' posting.

Since you have reconciled the bank accounts you should be able to run a report for the account, display and sort by 'cleared status', and find the open item(s) that are creating the balance.

Regardless of where they occur from - it is now necessary to add a credit to this account to clear the balance.  The debit side of this posting should go back to wherever you find the 'uncleared' problem originated from (using the report). Its is very likely that this is going to result in some type of income write-off in the current year to correct some prior year error.

OK now i'm a bit confused .. who is telling you to make these zero entries and why?

A 'zero deposit' sounds like a Journal Entry created from a different screen - but with the same result.

I gather you are trying to clean up and reconcile, so (in general) your question my be: where does the left-over trash go after the clean-up is complete.  Thats a common problem, especially with old messy books.  Once you have reviewed ALL the balance sheet accounts then the combined trash has to be dumped into some current year expense.  If you never identified the source of the trash then you cant really classify this expense - the 'unreconciled' account is the default dumping ground, but choose whatever you think is best.