When the demand for a product falls, the demand curve will shift to the left and when the supply increases the supply curve will shift to the right. That means, the curves will move to opposite directions, thus what will happen depends on the magnitude of the shift in the curves.
If the fall in demand is equal to the increase in supply, the equilibrium price will fall but the equilibrium quantity remains the same.
If the fall in demand of the product is greater than the supply increases, the relative shift in the demand curve is proportionately more than supply curve, thus leading to a fall in both equilibrium price and quantity.
If the fall in the demand of a product is less than the increase in supply, thee equilibrium price falls whereas equilibrium quantity rises.