I believe the answer is that it would act like a pendulum
as Potential energy is transfered to kinetic energy and back again. Gradually the energy would dissipate with friction until the eventually the stone would sit at the centre.
In other works it would fall reaching max velocity at the centre gradually lose speed until it reached the other side of the earth , not quite due to losses in friction then back again gradually losing height.
Cheers,
Peteai
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