Is the problem that emails sent from Discourse to the user are bouncing? If it is, you can find a record of the bounced email on your site’s Admin / Emails / Bounced page. If you click the link that is displayed in the last column on that page (the Email Type column), the bounce message that was returned from the user’s mail server will be displayed. That bounce message will often give details about what need to be done to resolve the issue on the mail server so that emails from Discourse can be delivered to the user.
It is unfortunate that the emails are not being marked as bounced by the mail server. If that was the case, Discourse would automatically stop sending them emails for a period of time after a few emails sent from Discourse had bounced.
For your case you may have to manually deactivate the user from their admin page.