One more question along these same lines. Is there a way to inset a particular surface while not extruding it?

For example I have this surface.



I want to do an inset, similar to the image attached, but I don't want to extrude it inwards. Bascially I want an inset but with a 0 height. I tried the seperate height option, but entering 0 would cause the tool to not work.