The messaging system built into DirectAdmin sends a message when a user is overlimit. The user gets the choice of whether or not she/he wants to be notified by email, or just through the message system.
But as Floyd points out, the problem is that once your user is suspended, there's no way to read the message, or even the email, unless the email is sent to an address of the server.
We recommend our users have an email address off the server, but we don't require it. Perhaps you should require it, as Floyd mentions.
Jeff