While creating a clock using two observers facing into each other, I found that by quickly breaking and then replacing a piston it leaves behind the head from the old one. This is probably not possible in survival because the player doesn't instantly destroy pistons.

I should mention that the leftover head is considered as an extended piston. Meaning that it cannot be pushed or interacted with. This only works when replacing with another piston (either regular or sticky) and no other blocks that I could find. It is not directional, nor clock dependent. This also happens vertically.

In the video below I demonstrate the process as stated above. My guess is that the piston head is fully extended and the base being replaced doesn't update the head to tell it the original base was destroyed, but now there is a new base. Also at the end of the clip I break one part and both pieces are destroyed, it applies to both ways. 

Edit: Optifine is not responsible for the problem. Confirmed on vanilla 1.14.4 and snapshot 19w37a.