Normally when a user leaves the company, you're going to delete the user's Person document from the NAB, add their user name to the Terminations group, and admin process will update all files that they may have had access to to remove them. Depending on how your server security is set, adding them to the Terminations group ad removing them from the NAB will prevent them from contacting the server and/or replicating and/or sending mail and/or signing onto Traveler or iNotes.
However, If the local machine in question is a user's personal machine, then there is not a lot you can do, because, unless the machine again contacts the server, it will remain in the state it was when they left; so they'll be able to open their mail file until their user.id expires.
So, one thought in this scenario - when creating user ID's, set them to expire in a short amount of time. It will cause you more work as an admin to update expiration dates much more frequently, but if you can expire a user's ID after say, 3 months, that will limit the time they can access it.
If there is a possibility that the user's PC will connect back to the server 'one last time', you can remove them from the ACL of their mail file, or better yet, set their ID to 'No Access'. But I think that will only work if you have 'Enforce a consistent Access Control List across all replicas'.