I am looking more into the use case when the incident is closed, but the end user replies to any notification to the email to get a response, whether the case is closed or resolved or even those "case has been updated notifications. 

so for further clarity: 
-incident is already closed

-user finds old email relating to incident and replies back to ask for help on something

-ServiceNow gets an email, and auto-replies that they replied to a closed ticket and to create a new ticket with the correct channels.