A. When the rubber rope reaches its original length, it begins to accelerate downward under the condition that gravity is greater than elasticity. When gravity and elasticity are equal, the acceleration is zero and the speed is the highest. Then gravity is less than elastic force, and slows down with the increase of acceleration. When it reaches the lowest point, the acceleration is maximum and the speed is zero. Therefore, A and C are wrong.

B, in the process of movement, gravity and the elastic force of the elastic rope do work, and the mechanical energy of the system composed of people and the elastic rope is conserved. So, B is wrong.

D when a person falls from the original length of the static elastic rope, the acceleration at the initial position is g, and according to the symmetry, the acceleration at the lowest point is g, and the direction is vertical upward. When an object falls from a certain height, the lowest point is lower. According to Newton's second law, the acceleration is greater than g, so d is correct.

So choose D.