If you are sent messages while your inbox is full, The sender's mail server should continue to try and send the email for about 30 hours before failing, but this cannot be guaranteed. If the sending email has too many failed attempts the sender will then receive a bounce-back message notifying them that the email was unsuccessful and the sender will have to manually resend the message.

To correct the problem and make more space available, please read the following article: http://support.bigblackbag.com/KB/a48/my-email-is-failing-being-rejected-because-my-inbox.aspx