A matter of policy

This has been a long standing policy in Technical Services, dating to the previous VP-IT and endorsed by the current one. This policy concerns email like this, generally from a manager of some kind:
"[Person X] no longer works here. Please change their password and give it to [Person Y] so they can handle email. And please set an out-of-office rule notifiying people of [Person X's] absence."
To which we politely decline. What we will do is set the out-of-office rule, that's just fine. We'll also either give a PST extract of Person X's mailbox, or if there really is no other way (the person was the Coordinator of the Z's for 20+ years and handled all the communications themselves before retiring/dying) we'll grant read-access to the mailbox to another person, and effectively turn the Person X account into a group account but lacking send-as rights.

What we will categorically not do is change a password for an inactive user and give the login to someone else. It comes down to identity theft. If we give Person Y the login info for Person X, Person Y can send email impersonating Person X. And that is wrong on a number of levels.

We resist giving access to the mailbox as well, since a non-trivial proportion of end-users give their work email as the email address for web-registration pages all over the internet. And thus that's where the "password reminder" emails get sent. Having access to someone else's mailbox is a good way to start the process of hacking an identity.

Yes, we do occasionally get a high level manager pushing us on this. But once we explain our rationalle, they've backed down so far. There is a reason we say no when we say no.