You have a workflow set up where tickets are assigned to a particular agent depending upon the job description, the group this concerned agent belongs to and the expertise as well. Sometimes an agent would need another agent to look into something in the thread or receive notifications to go through the discussion. 

In this case, an agent could be added as a "watcher" who would receive all the notifications about the thread from the time when the agent is added as a watcher. You could have multiple agents added to a ticket as watchers.

Only the one added as a watcher could remove oneself from the thread. An occasional agent without a day pass could still follow the ticket in the email thread when added as a watcher on tickets.