When an e-mail is sent to non-existing address, the last SMTP server that accepted the message for delivery (which is your SMTP server in most cases) should generate a non-delivery report (or delivery status notification) and mail it to the the sender's e-mail address.
These reports can be downloaded and parsed using Rebex Secure Mail's POP3 or IMAP and MailMessage object and a DSN parser found in another forum post. Some SMTP servers also make it possible to request a notification when the message has been delivered successfully (this is also explained in the forum post).