The unemployment rate counts only those who participate in the labor market. It seems that millions of people have "stopped participating in the labor market". The government says they have stopped looking for work, therefore are no longer unemployed. How does the federal government determine this status?

Here's my understanding, please tell me if I am wrong: If you lose your job, and file for unemployment, you are officially unemployed. After you have used up all your benefits, and stop contacting the unemployment office, you have "dropped out of the labor market".

I think there is a vast difference between staying in contact with a government bureaucracy that is of little or no help, and not looking for work.  As far as I can tell the unemployment numbers are just those who are collecting, and those that have used up their benefits don't count any more, big brother says you quit trying. The chart below is much more indicative of the current situation than those still able to pull a check from Uncle Sam.