Flailing wildly around again.
Lets see. Rockets can escape gravitational pull by getting further away from earth. So I suppose acceleration due to gravity increases as you head nearer the centre of the earth.
You drop something from the surface and its acceleration increases all the way to the centre. It overshoots due to momentum but (decaying acceleration due to gravity) pulls it back towards the centre where it overshoots again - but to lesser degree.
In theory this would go on forever - with ever diminishing overshoot
??