Here we have the data series from FRED for the unemployed, segmented by duration. It is a bit busy, so what we are looking at here is the proportion of the 100% of the unemployed that each duration segment is contributing to that total...with the absolute number of each segment as the label for each month as well.
With respect to the longest term unemployed data segment, 27 Weeks and Over, is declining in both the absolute number and the relative contribution. On a month over month basis, the trend is also solidly in decline. But is the reason for this decline improvements in the labor market or workers exiting the labor force?
Looking at the change in PAYEMS, the total non-farm payroll in thousands of employees, the answer appears to be exit...
And finally, as a lagniappe for a negative interpretaion of the decline in UEMPMED, it appears that there was a big jump in the in the unemployed between 1-3 months, UEMP5TO14.
To recap on reasons for the decline in UEMPMED:
1. The longest term unemployed are declining according to the current counting methodology
2. They are almost certainly exiting the labor force as non-farm payrolls are flat over the period of the big declines in UEMPMED
3. A significant increase in the UE duration segment of between 1-3 months is also pulling the median down