Pre-print, Working paper: This paper studies the theoretical link between real wage rigidity and the destabilizing mechanism driven by the countercyclical precautionary saving demand against unemployment risk. First, I analytically show that destabilizing supply-demand feedback is a general equilibrium outcome of rigid labor cost adjustments. Second, the calibrated wage rigidity consistent with empirical labor market dynamics suggests that real wages are less likely to be sufficiently rigid to cause the destabilizing mechanism. Finally, the way we model job destruction dynamics can have a fundamental impact on the range of real wage rigidity consistent with empirical labor market dynamics and, thus, economic dynamics. Therefore, in contrast to the presumption of many researchers, assuming exogenous job destruction is not innocuous.