You will need the Profile Archive permission to perform this action.
An archived profile becomes read-only and is unable to have any current involvement. An archived profile will still count toward your profile quota.
There are multiple ways to archive a person profile.
From Their Profile
Navigate to their profile and click on "Actions > Archive" in the upper right area.
A pop up will appear asking you for the reason this person is being archived. Complete the required fields, and click on "Archive" to complete the action. These answers will be added as a note to the person's profile.
In Bulk
You will need both the People Archive and Reporting permission to archive in bulk.
Navigate to the People Query Builder in the left-hand menu, via Reporting > Query Builder > People, and construct a query that returns the people you are interested in archiving.
Next, click on "Mass Change" from the "Actions" menu right above the results area.
In the pop up that appears, select "Archive" from the "perform an action on profile" drop down.
A pop up will appear asking you for the reason you are archiving these people. Enter the required information, and click on "Done." You will be taken back to the "Perform Mass Change" pop up.
Finally, click on the update button to perform the bulk archive. The archive reason will be added as a note on the profiles that were archived.
