The real question is what "labor component" is left out of the determination, which is the point. I understand "who" is considered unemployed...but the question put forth was "Is there a componenet of "unemployed" labor left out of the unemployment rate calculation?"
Yes, the BEA. w/o regard to the BLS, tracks all national economic statistics from manufacturing output to labor. usage...
Yes, and people whose unemployment benefits have run out are not, because failure to qualify for benefits is not a determining factor.