The bottom of the Slinky remains at the same position because upwards-pulling tension in the spring cancels out the downwards-pulling force of gravity. When the top of the Slinky is released, gravity pulls the top of the Slinky downwards until it has fully collapsed (no more tension) and falls to the ground. The center of gravity of the Slinky falls with the same gravitational acceleration experienced by any dropped object.
Source: https://youtu.be/8UimHnsWSBc
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