In fact, the gravity near the center of a planet goes to zero, since the surrounding mass is warping spacetime equally in all directions.
Assuming we had a magical drill, the drilled hole would immediately collapse due to gravity.
Assuming there would be a magic force preventing the collapse, the ball should stay in the center of the hole as there is net zero gravity right at the center. The inertia could let it overshoot a bit, but it would be pulled back as it possesses a negligible mass compared to the heavy object and therefore its inertia is quite small compared to the gravitational forces.