As a systems administrator and corporate worker, this is not the correct way to do this.
As other people have stated, the email is company property and can be dealt with in any manner they feel proper.
I am writing this from a Microsoft perspective, but this applies to everything. Do not change the password. The account should be disabled. This will prevent anyone from logging in as that user. Do not delete the account from Active Directory, as this can cause dangling SIDs. This means, any documents created, edited, associated with that user still show that user properly. A knowledgeable systems administrator should know how to deal with this.
As for the email itself, generally you give another user read access to that email box and add it to their email client. This allows the user to read old email, as there may be important information in there that needs to be referred to. That user can then reply to old or new mail to he terminated user, with their own email stating that the old user is no longer with the company and that they are assuming responsibility for future contact.
Forwarding email to a shared group is not a good idea in general, as people can assume someone else is taking care of it and no one ends up replying. Or just as bad, multiple reply to an incoming email. One point of contact is the best way to go, unless there is some sort of ticketing system associated with the redirected email.
Depending in your business, local and federal laws, etc, you may be required to keep email for a certain amount of time. Check with HR and/or your legal team to see if there are any requirements that need to be met.