When an email user leaves your organisation, we recommend initially changing the password for their account (the link contains a step-by-step guide), ensuring security on that side of things.
Subsequently, you may want to download copies of their email, and replace their account with an alias, forwarding any mail they receive to a different address. Here's how to delete and replace an account:
1: Log in to ESA as an administrator.
2: Click the relevant account in the User List.
3: Double check that you're deleting the right account.
4: Click the Delete Account button.
5: Click Create User in the top left of the interface.
6: Select Alias from the drop down on the right.
7: Enter the chosen Username - the first part of the email address.
8: Add the forwarding address in the Copy Mail to section - select from internal mailboxes with the dropdown, or type in any external address.