The birth/dealth model has nothing to do with the weekly jobless claims number. The weekly number is the actual number of people who file for unemployment and is reported by the Department of Labor.
The birth/death model is a part of the analysis that goes into the monthly net change in nonfarm payrolls report, more commonly referred to as the employment report or jobs report. This is produced by an entirely different agency, the Bureau of Labor Statistics.
So, as macrie said above, there are those who find employment who offset those who are filing initial jobless claims. In May, for example, the average weekly jobless claims were about 630,000, yet for the month as a whole the economy shed roughly 345,000 jobs.