I see the fall of the slinky as a superposition of two motions: (i) a fall of the centre of mass of the slinky, and, (ii) a compression of the slinky. It seems that the slinky that we see has the property that the sum of these motions leads to a stationary lower end. I can imagine a somewhat-slinky-like spring with different elastic properties for which that cancellation does not occur.
This VDO clips talks about surprising facts about a falling slinky