Rule action to mute unsubscribe conversation

Part of our workflow is that if emails come into individual inboxes, we created company rules that if they are not HR-related emails, they will go into a shared inbox. However, we noticed that it is still in the "shared with me" inbox. The point of all this is to minimize email conversations individual's total inbox as a whole. So we want to create a rule for it not to show in the "shared with me inbox". unless they are reassigned to or were @mentioned in the conversation.

After a rule to auto-unsubscribe based on any condition (eg. Tag added)

We would like this rule implementing to allow Front Live Chat users to be auto unsubscribed once a chat has been assigned