Whether one has exhausted their unemployment insurance benefits has nothing to do with the official Bureau of Labor Statistics (BLS) headline unemployment rate that comes out the first Friday of every month and is widely headlined in the media. That is a myth that will sadly never die. The official headline unemployment rate is based on a monthly household survey of 60,000 households. They count people as unemployed if they are not employed, *and* they tell the suveyor that they have looked for work sometime in the past 4 weeks.
For much more on this, including what constitutes looking for work (pretty lenient standards, but still involve more activity than simply reading job ads) see: http://www.bls.gov/cps/cps_htgm.htm
On the other hand, the official unemployment rate does not count people who have not looked for work in the past 4 weeks, nor does it count people who are part-time employed that are looking for full-time work. (There is a separate figure, also often reported deep down in news articles, the underemployment rate, that counts these 2 groups as well as the "officially" unemployed .
So yes, the official unemployment rate undoubtedly undercounts the number of unemployed people by most standards.
On the other hand, if I were unemployed and still collecting unemployment insurance benefits or other government benefits that were contingent on me making a good faith effort to find work, I would be very reluctant to tell a government surveyor that I haven't made any effort to look for work during the past 4 weeks. i.e. some people who are not employed and not really looking for work, but tell the surveyor they are looking for work, are counted as officially unemployed....
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