Many email systems (sendmail, postfix, and others) support the idea of "address extensions". For example, let's assume my address is "email@example.com". If my mailer supports address extensions, I may also be able to send email to "firstname.lastname@example.org". The mail still goes to the same places, but the extension is available for filtering. The mail environment feeding a ticket system could be configured with '_' as the extension separator, so that anything addressed to email@example.com would get forwarded to the ticketing system, which would use the address extension ("1234") to match the email to an issue.
Another mechanism is to dedicate an entire subdomain to the ticketing system. In this case, instead of email going to firstname.lastname@example.org, maybe it would go to email@example.com. The example.com mail system would be configured to pass all email for support.example.com to the ticket system.
All of these models are used in practice.