How To Perform
One method is for the player to run at an edge, and tilt the control stick at a slight downward angle, but not too far down, or else the player will stop and start to crouch. If done correctly, the player should still be running without falling off the edge.
The player can also do this by tilting the control stick in the direction they want to run about halfway, but not too far back.
Usually, characters only walk/run off edges when the Control Stick is mostly or fully sideways. Characters can also continue to run if the Control Stick is relaxed slightly. By combining these two tolerances, it's possible to find a Stick position that allows a character to continue to run, but does not allow the character to run off edges.