Symbiosis: Exim can't deliver to a virgin mailbox
Mostly, Exim hands off email to dovecot for delivery. BUT, it's possible to use an Exim filter file to ask Exim to deliver email directly to a mailbox.
If Exim tries to do that before Dovecot has delivered to that user, Exim will fail.
Dovecot lazily (ie, when it first delivers an email to a user) creates a quota file in the root of the user's mailbox. Exim can't deliver email to a user if that quota file is missing. And it can't create it either.
This only matters if the user doesn't get mail delivered by dovecot, which is kind of unusual. The simple work-around is just to send an unfiltered email to the user.
A better fix might be to have a cron job looking for missing quota files, and adding them where required. Or maybe there's an Exim option to ignore the missing file? Or something.