When an e-mail address is bouncing back the automated discourse e-mails, this seems like you wouldn’t necessarily need/want to silence or delete their account for that unless you suspect it is a spoof account or something without valid e-mail.
Guess that is probably the reason why you would want to put account on hold temporarily to validate they have working e-mail, do you have a high volume of cases like that or is it practical to deal with those one on one manually?
There are some other options like manually changing e-mail notification settings, or changing the not-working e-mail address to other working address controlled by admin or something temporarily. That may not be the best idea just some random ideas here.
When an account is deleted that doesn’t send e-mail notification about that last time I checked. Simple but kind of brutal policy is to delete accounts if they don’t have working e-mail.