Edgebug is a glitch in the engine that allows you to fall down a long distance without taking any damage, by hitting the exact edge/brush of a certain block. It is easy to do on stairs or other broad edges.
The engine applies the fall damage if the check if the player is on ground succeeds. Such checks are done at the end of movement frames. When you perform an edgebug, you start in mid-air and end in mid-air in one movement frame, while sliding off of an edge happens in-between. The game never knows if you were on the ground or not, thus never applying any fall damage.
It doesn't matter if you are ducked or not in order to perform an edgebug.