Employment falls when either labor supply shifts to the left, or labor demand shifts to the left, or both [for these purposes, "labor supply" includes any labor market distortions, such as income taxes and minimum wages]. This is a tautology -- it is true regardless of what is the "right" model of the economy, and regardless of what really caused the recession.
Thus, it is no surprise that recessions tend to have (a) negative productivity growth and (b) leftward shifts of the labor supply curve. The former is related to labor demand and the latter to labor supply. If we just focus on employment reduction events, it is no surprise that the average event has both reduced labor supply and labor demand.
What would be VERY interesting is a recession that occurred with only ONE of these changes. The prototypical real business cycle featured productivity shocks and a stable labor supply function (more precisely, a labor supply function that shifted ONLY due to wealth or intertemporal substitution effects) -- in other words a real business cycle recession is one in which the reduction in employment is largely blamed on labor demand. That is why commentators on (critics of?) the real business cycle model have repeatedly illustrated that employment fluctuations have to be explained in part by labor supply shifts (Barro and King, 1984; Hall, 1997; Mulligan 2005), and not just productivity shocks.
This recession may be one of the first ever that can be explained by ONE of those changes. But, contrary to prototype real business cycle, the ONE change is in labor supply without much reduction in labor demand. The basic methodology of real business cycle theory may apply well to this recession -- as long as we put the shock on the labor supply side of the market and hold productivity constant.