hmm. I thought it worked like this "Persons are classified as unemployed if they do not have a job, have actively looked for work in the prior 4 weeks, and are currently available for work." [1]
and
"Discouraged workers are a subset of persons marginally attached to the labor force. The marginally attached are those persons not in the labor force who want and are available for work, and who have looked for a job sometime in the prior 12 months, but were not counted as unemployed because they had not searched for work in the 4 weeks preceding the survey."
I don't think it's connected to insurance benefits. I think the statistic is dumb, because it should count people who are available to work but aren't.
On the other hand, if you aren't looking, maybe you really aren't available.