If the ball, the cliff, and the ground are all on the Earth, and everything is bathed in an ocean of air, then the ball's acceleration will decrease as it falls, because of the friction of air resistance. If it has far enough to fall, it's possible that its acceleration may even become zero, and the ball settle on a constant speed (called "terminal velocity") before it hits the ground.
But until we get to College-level Physics and Engineering, we ALWAYS ignore that stuff, and assume NO AIR RESISTANCE. The ball is in FREE FALL, and the ONLY force acting on it is the force of gravity. We also assume that the distance of the fall is small enough so that the value of gravity is constant over the entire fall.
Under those assumptions, there's nothing present to change the acceleration of the falling ball. It's 9.81 m/s² when it rolls off the edge of the cliff, and it's 9.81 m/s² when it hits the ground.
