If you stop looking for jobs you are not considered unemployed as someone not actively seeking work is not considered to be in the labor force. That is a different issue entirely and you will have to look at a different statistic. There are different types of "unemployment rate" and maybe what you want is U-4 or U-5 which include discouraged workers. Either way you can not expect a single number to encapsulate something as large and complex as the US labor market.