Is there a way to configure E2C to reopen closed cases when case email hits the case after its close?

 

Our business problem is as follows:

 

Sometimes team members are absent [sick, travel, etc]. During such absence, we have a need to know of email activity tied to that person's cases. This is not a problem for open cases since they are easily identified and transferred (ownership). My thought is if we could set a global rule where all case email triggers reopening a case if that case is closed, it would solve this problem.