Best practices for handling change of email auto-replies when there’s a user account

Scenario: the Example company has some sort of front-end system that uses the customer's email address as the user ID.

Example.com sends a marketing email to bob@harvard.com (which would be Bob's user ID on Example.com), and gets back an auto-reply that Bob is no longer at Harvard and that all communication should now go to bob@yale.com.

How is such a thing typically handled? Is there an expectation that all communications from Example.com should now go to bob@yale.com - especially since Bob's account on the web site is still bob@harvard.com?