Supply can still matter. In a world of unemployed resources, imagine a company called Apple invents a device called — improbably — an iPad. That's a positive supply shock. People will be led to spend more money. The inventors and their employees will have more money to spend. There will be a positive multiplier throughout the economy, as analyzed by W.H. Hutt. First aggregate supply went up and then aggregate demand went up. It's all one step on the way to economic recovery.
Starting with insufficient aggregate demand does not cut off this process. Starting with a liquidity trap, in contrast, would prevent this multiplier from picking up any steam, if you could sell the iPads in the first place that is.
One bottom line is that aggregate supply still matters when aggregate demand is insufficient. Another lesson is that positive supply developments can increase output and employment.