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In this paper, we investigate the motion of a particle confined between the oscillating and fixed walls. As the particle collides with the moving wall in the phase of oscillations, when the wall velocity grows, the wall after collision catches up with the particle. This process can be repeated many times until in finite time interval the particle is found lying on the wall and continues its motion together with the wall. When the sign of the wall acceleration changes the particle detaches from the wall with zero velocity, so that it looks as if the particle "sticks" to the wall. It has been found that if the collision is inelastic, "sticking" leads to convergence of close trajectories except for the case of weak decay. On the contrary, in the case of elastic collision "sticking" of the particle causes even a more rapid divergence of theses trajectories.