Mysterious Slinky

As seen in the video, the lower end will stay at its place , until the slinky achieves its natural length. Thereafter, it fall as a whole in natural length.

This can be explained by Newton's first law of motion also known as the law of inertia which states that:

An object at rest will remain at rest and an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The slinky is so flexible that we can consider every small length of it as a separate object. Before release, its lower end is at rest, therefore, when it is released the lower end stay at rest. There is no unbalanced force acting on the lower end because the gravitational force acting on the upper portion of the slinky is balanced in accelerating the upper portion according to Newton's second law of motion or $F=ma$ in short. In other words, the potential energy lost by the upper portion is converted to kinetic energy in the upper portion hence there is no energy difference in the lower end initially. This will happen until the slinky achieves its natural length when no loose portion can be accelerated anymore then the slinky as a whole has to accelerated downward.

This is somewhat similar to what would happen if the Sun were to vanish suddenly. It'd take about 8 minutes before the Earth starts to behave differently. The sudden change in tension of the spring at the top when it is released takes a while to get to the bottom of the slinky, which is still being held up by the tension it had before the release. This is a simplified explanation, not the full proof.