Dear Maya Benoit,
Thanks for your posted idea.
Your suggestion does read like an email notification functionality that already exists, e.g. the Trados Team system is sending email notifications for when a task assignee accepts or rejects a task.
An overview for all notifications can be found at Email notification messages, incl. a description on what triggers and who receives the notification, e.g. for task rejected by the assignee:
Should these notifications not work for you, then please reach out to our Support team for troubleshooting.
Many thanks,
Phillip Maieski | Trados Product Management