When both supply and demand fall, the effect on price can be unpredictable. If supply drops more sharply than demand, prices may rise. But if demand falls faster, prices could drop. It all depends on the rate of decline.
For example, during a recession, people buy less (demand falls), and businesses cut production (supply falls). Depending on the severity of each, the market adjusts differently. Economists study these shifts to predict outcomes and adjust policy.