Of course, it also depends on why the host institution doesn't recognize them. In AGDee's example, I wouldn't define the U of Toronto chapter as an underground chapter, because the school doesn't recognize Greek organizations in general.
But at my school, we have a national organization who has lost university recognition (and has not regained it after several years) but continues to maintain their charter from their national. Because there are other Greek orgs that are recognized on campus, our IFC and Greek advisor discourage men from rushing that house because they do not have any of the benefits of university affiliation. Although they are still recognized as a chapter, I would consider this more of an "underground" situation than the first.
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