If someone gives up looking for work they are still unemployed.
Actually according to BLS methodology you are no longer unemployed in that situation.
Yes - still unemployed ... but not registered with one of the state unemployment agencies - most of the time called ‘Work Force” blah blah blah.
Also - from experience - if a person was self-employed even as something like a consultant or manufacturers rep. or as an owner of a larger firm and is now BUST - no customers - no income ... he/she does not get any state assistance for unemployment insurance in most states ... and he/she is likely not registered... so not counted.
Yes folks, a self employed person can be unemployed for months and years after having a business failure ... BUST and he/she gets NO ASSISTANCE... no bailouts period.