From Unemployed to Discouraged

Suppose someone is officially unemployed. That is they don’t have a job, but they are actively looking and willing to work. They are counted in U in this diagram.
But suppose that after awhile this person decides the chances of finding a job are pretty poor. They are still willing to work, but they quit actively looking. At this point, they are no longer counted in U, the Unemployed. They have now moved into the Discouraged Worker category, which is not part of the labor force. So both U and L decline.
.

Suppose someone is officially unemployed. That is they don’t have a job, but they are actively looking and willing to work. They are counted in U in this diagram.