The unemployment rate n America does not count those whose benefits ran out and no longer draw money out (the Europeans count everyone because their benefits never run out). The real figure is probably much higher - thank god we have the underground industry to absorb many of these displaced workers - drugs and sex industry.
If you're "looking" for work then you are counted among the unemployed. And, as you suggested, there are people who are "officially looking", but who have "other" income, and are counted nonetheless.