Since the interior of Earth is made of molten (liquid) rock it is not possible to dig such a tunnel.
However, if we pretend that Earth is simply made of rock and that such a tunnel exists, a ball dropped down the hole would eventually come back. This is due to the nature of the gravitational forces between the ball and Earth.
When the ball is dropped, the force of gravity pulls it down into the hole. As the ball falls farther toward the center of the Earth, the gravitational pull of Earth on the ball becomes less and less. This is because gravitational force due to all of the mass of Earth - which is farther away from the center of Earth than the ball is - cancels itself out and only the mass closer to the center produces a gravitational force on the ball.
Eventually when the ball reaches Earth’s center, all of Earth’s mass is farther from the center than the ball is and the force due to gravity is zero. The ball, however, is still moving vary fast and begins to move away from the center of the Earth.
As it moves away from the center, the mass closer to the center than the ball increases as does the force due to gravity. This force is now trying to pull the ball back toward the center.
The ball slows down, bit by it, until it reaches the surface once again, where it slows to a stop.
Gravity pulls the ball down and it once again falls down the tunnel.
This process would go on indefinitely unless there were some other force (such as air-resistance) to stop it.