[Steven W.]

How can the "unemployment" stats remain constant when jobs are being elimated?

because they're two sides of the coin - new jobs are created while others are eliminated, in this case the net offset negated each other (but is errantly described as a "plunge" out of apparent bias by the author)

[familyofman]

"new jobs are created while others are eliminated, in this case the net offset negated each other " in a manner of speaking. The calculation of "unemployed" involves a number of metrics; size of available workforce, number of jobs filled, new jobs created, jobs eliminated. For most analysts the unemployment rate is a useful number, but is not as important as the "net jobs created" - which fell again. The current estimate is that there has been a net loss of over 2.4 million jobs over the last 2 years.
Not included in the analysis is the fact that the avaolable labor pool was decreased by the number of National Guard & Reserves called up - no one has a real good handle on that because it's not normally considered. There was what is known as the "jobless recovery" of the early nineties where the unemployment rate remained constant even while jobs were being created.