With the sudden fall in the firm’s output demand, the supply has to be lowered. The lower supply in the market means overproduced final goods adding to the inventory. Thus, the inventory will not decrease with a decrease in output demand.
So, in the case of a sudden fall in demand, the inventory stock cannot remain the same.
It is a stock concept. Firms accumulate inventory to meet consumer demand in times of shortage. It has nothing to do with the current price level. Therefore, a firm’s inventory will not increase or remain the same depending on the price level.