All positions are automatically moved over to the Archive at the time of Unposting. This can be accessed by first clicking on My Positions, then on the right-hand side of the screen, the "Archive" tab.
All previously Posted positions are here, as are the applicants. The processing functionality remains exactly the same as the normal Applicant Queue, so technically you can even Hire applicants from the Archive. The only difference is both the position and applicants will have a red disclaimer text to clarify they are Archived or associated with a position you are no longer actively recruiting for.
Once a position has been Unposted and moved to the Archive, it cannot be removed or un-Archived.