Perhaps I'm wrong, but I believe the Directory Import Automation is a standard feature and not too difficult to configure: https://www.qualtrics.com/support/employee-experience/directories/employee-directory-import-automations/. I'd strongly encourage having your Directory updated every day. Pair that with a Lifecycle project (which you may have to pay for if not already part of your license) https://www.qualtrics.com/support/employee-experience/getting-started-employee-experience/getting-started-employee-lifecycle/getting-started-with-employee-lifecycle/, and you have a very simple setup that's fully automated.
Without a constantly updated Directory, you're most likely looking at (1) an admin loading participants each week and scheduling invites or (2) providing exiting employees with an anonymous link in their offboarding materials. The former creates not only more administrative burden on a weekly basis, but also an undesirable delay in reaching exiting employees. The latter would suffer from the need for employees to "opt into" the survey (a link buried among many other exit materials feels a lot more "optional" than a link in an email specifically focused on the exit survey) as well as the need for them to respond to demographic questions in the survey to capture the unknown data.