It does not include those who have given up looking for work or don't consider the available work sufficiently rewarding. A sufficiently strong recovery brings more of those to find work.
Labor force participation may be a better measure. https://data.bls.gov/pdq/SurveyOutputServlet
> Broader measures of unemployment tell the same story. The so-called U-6 rate, which captures people who are working part-time but want a full-time job, and those who would like a job but have given up looking out of frustration, is also back down to its level before the last recession. It fell to 8.6 percent in April from 8.9 percent, and the last time it was lower was November 2007.
It seems intuitively likely to me that structural unemployment is becoming a bigger problem (and that structural rather than cyclical factors are an increasing factor in discouraged workers.)
"Full employment" doesn't mean no employment problems, it just means that the problems are non-cyclical.