When consumer demand reduces, and if companies could reduce prices to bring up demand during a recession, then why there is less production/output and more unemployment during a recession?
Draw a demand and supply curve and shift the demand curve downwards.
You will see that the new equilibrium has lower price and lower quantity, so although prices are lower (which means that the initial drop in demand is partially compensated), total output nevertheless decreases and therefore the required amount of inputs will also be lower.
So, while firms might lower their prices to increase demand after a drop, they will never do this to the point where demand is equal to the level before the reduction. As a result, output will decrease.