I knew a foreigner in the astronomy department at the university here who was a "post-postdoc" independent researcher. How could she have her own office in the astronomy department as an independent researcher?
Many universities offer positions with titles such as "research professor" or "staff scientist" or other similar titles. These all indicate the same basic phenomenon: a researcher who is generally supported by "soft money" (In other words, a position subject to sufficient funding), but who is otherwise more or less "permanent" staff. Such scientists may or may not have their own dedicated office space, depending upon overall space constraints within the department and within their boss's research group.
Such possibilities depend a lot on recommendations and past achievements of such a researcher.
If one is a real scientist with good publications and good, interesting project, not only office space, but also laboratory access and resources like access to the supercomputing facility may be provided.
Most obvious, a researcher may be supported by his home institution (industrial or educational) and would not require also salary for the project.
The similar situation may also result from various funding schemes that allow to obtain the initial grant for a position easily, but make progressively difficult to extend it over time, regardless of achievements like publications. In such cases some researchers actually work for free for a limited time in institutions that are no longer able to employ them, to finish everything properly.