A major challenge for advanced propulsion and combustion technologies is obtaining stable combustion with a wide range of reactant compositions and temperatures. Being able to predict the combustion stability, flow structure and flame location based on a distinctive property of the reactants would be extremely valuable. Recent experimental measurements in two different combustor geometries showed that both the flow structure and stability map collapse using the flame extinction strain rate or strained consumption speed. In the present study, the origin of those results is investigated using detailed numerical simulations of wake stabilized laminar lean premixed flames with a wide range of reactants compositions and temperatures. The results reveal the underlying feedback mechanism between the flame and the flow field. The analysis shows the significant impact of the flame response to stretch on flame stabilization and associated flow structure. Capturing similar scaling of the characteristic chemical and flow time scales in both turbulent and laminar premixed flames indicates that the findings have a fundamental origin. The findings can be extremely useful for other combustors in which the combustion instabilities originate from the flame-vortex interaction and there is a need to operate with different fuels and inlet conditions.