To replicate I put a wooden slab on cobblestone and on top of the wooden slab a cobblestone slab.

I used a pickaxe to remove the cobblestone slab, both slabs seemed to vanish, but instead they were still there as thin air. Had to use /setblock command to get rid of the "ghost" slabs. You can't see the salbs and there are no dropped slab items in the world, but they still have collision.

So it's not possible to disasamble slabs of different material - this doesn't happen if both slabs are from the same material e.g. both are cobblestone.

Edit:
It also seems that I can't place a vertical slab (of cobblestone) while I'm sneaking.