Whenever a user reaches their quota, they can no longer access their email account to delete messages and thus reduce their quota usage. The error that usually appears is "IMAP command SELECT failed." I'm guessing this occurs since there is no space left in the users account for temporary files, indexes, etc.
I haven't tested to see if POP access works in this situation, but I would not consider that a valid workaround. IMAP is used by many of my users, especially those using SquirrelMail or Horde (since webmail by default uses IMAP), so these applications are essentially unusable once they reach their quota. The only workaround I have come up with is to have an administrator manually increase their quota temporarily so they can log in and delete their messages.
Technically, I'm not sure if this is a Virtualmin/Webmin bug or a Dovecot bug. Nevertheless, it is a core function of virtualmin to support IMAP with quotas, and Dovecot is the server of choice, so we need to figure out a way to make it work.