When standing on soul sand and attempting to place a slab adjacent to it while you would be clipping through the slab, you can fall through it.
Here's a video that explains it better: https://youtu.be/xE8occgJUhM
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From a number of blocks with different hitboxes, upwards-facing slabs are the only block which you can place while clipping in (at least, using this method).

The block the player stands on can be anything with height >=0,5 and <1. So it also affects lower slabs.
Confirmed for 1.9.3-pre1.
When sneaking from the lower slab previously stood on, you shouldn't normally be able to go down if the height difference is more than a block or so, but if the other slab is inside you, you can (and fall to your death). Is this another part of the bug or another bug?

Resolved as a duplicate of MC-116877 because of a better description
Falling through blocks you are standing inside is not a valid bug. However, you should not be able to place blocks inside yourself. Does this only affect top slabs or are you also able to place full blocks adjacent to soul sand while standing "inside" them?