When a user leaves the company before doing anything else you should deactivate their Office installations so that the existing install can be assigned to a new user.  If you don’t do this, Microsoft recommends uninstalling and reinstalling Office.

I’ve found that you can trigger a new user activation of Office by modifying the following key:

HKEY_LOCAL_MACHINE\SOFTWARE\
Microsoft\Office\
ClickToRun\Configuration\O365BusinessRetail.EmailAddress

Upon opening any Office application it asks to activate like a fresh installation.