While a properly inflated basketball returns a good fraction of the energy it receives while other balls may not. In fact, a bowling ball of the candlepin variety bounces pretty well from a hard surface such as cement. But when it hits a softer surface such as wood, the wood receives much of its energy and wastes that energy as thermal energy. The simplest kind of interaction is a collision or impact. There should be some quantity during a collision.
Some property carried by the objects is unaffected by the collision and is therefore preserved.
Remember the direction as well as the magnitude of the velocity must be considered. The force acting upon the object whose momentum is changing must be external to the object. No amount of motion within the object, no matter how violent, can change the product of its mass and velocity. With no external forces, momentum is conserved. Mechanical energy is also conserved.