Recipients of basic income would not need to be unemployed, working, or searching for work. Workers and unemployed people would both receive basic income without question. Receipt of basic income does not depend upon your savings thus you can receive the benefit regardless of savings or other capital. There is no way a person can forfeit receipt of basic income. When people state it is "unconditional" they really mean it, thus in addition to calling it "basic income" people often call it "unconditional basic income" or "universal basic income guarantee" or other variations.
There have been some temporary successful basic income tests, on small populations, but in the year 2013 basic income has not yet been implemented in a widespread or permanent manner. Times are however changing, there is White House petition (archive) for the implementation of basic income (15th December 2013 deadline), and a Swiss referendum is pending regarding the implementation of basic income.
Importantly I want to draw your attention to how the "philosopher, logician, mathematician, historian, and social critic" Bertrand Russell advocated basic income. Bertrand Russell is noteworthy person who has deeply considered the issue of receiving money without needing to work. Bertrand Russell did not actually use the words "basic income" (basic income is a new phrase) but Bertrand Russell did advocate an unconditional income for all people, which would leave people "free" if they decided they didn't want to do any work.
On page 102 of "Proposed Roads to Freedom," accessible via Project Gutenberg (free online library), Bertrand Russell stated (bold emphasis added): "When education is finished no one should be COMPELLED to work." Bertrand Russell believed people should be "completely free" from the need or obligation to work. The document in question, Proposed Roads to Freedom, is also freely available via zpub.com (archived). Below is the relevant excerpt from Proposed Roads to Freedom (first published in 1918):
"When education is finished no one should be COMPELLED to work, and those who choose not to work should receive a bare livelihood, and be left completely free; but probably it would be desirable that there should be a strong public opinion in favor of work, so that only comparatively few should choose idleness. One great advantage of making idleness economically possible is that it would afford a powerful motive for making work not disagreeable; and no community where most work is disagreeable can be said to have found a solution of economic problems. I think it is reasonable to assume that few would choose idleness, in view of the fact that even now at least nine out of ten of those who have (say) 100 pounds a year from investments prefer to increase their income by paid work."
The psychoanalyst Erich Fromm also allegedly supported the idea of basic income. Fromm apparently advocated basic income in his books "Ways Out of a Sick Society" and "To Have or to Be?" but unfortunately, after some online searching, I haven't found any significant corroboration of Fromm's support for basic income. If you have access to the aforementioned books by Fromm perhaps you could post copies of the relevant excerpts online.