If the edge of the drop-off is at a certain angle oblique to your line of travel and your cane tip happens to reach just short of it, you will have warning of the drop-off one step earlier when walking "in step" than you would when walking "out of step."
That is, if you are using "constant-contact" cane technique (sliding the tip of the cane along the ground) in this scenario and you are walking "out of step," the cane will not reach the drop-off until your forward foot is one step closer to the edge than it would if you were walking "in step." If you are using "touch technique" (touching the ground only at the end of each arc) in this scenario, when walking "in step" the cane goes over the edge one step before you do, whereas when walking "out of step" you may not realize the cane has gone over the edge until you have stepped over it yourself.
This principle is illustrated below with videos and photos.
VIDEOS:
The video to the right just shows the cane which is used in the demonstration of the second video (it's 50 inches long, moved in an arc 6 inches wider than the body).
The videos below show what happens when approaching a diagonal drop-off when walking with the cane "in step" and "out of step." In the video to the left below, a cat who is sitting patiently but with interest on the carpet that represents the "drop-off" could be considered a dangerous lion waiting for anyone to fall off the edge! The video below to the right shows the same demonstration while describing a few of the movements verbally.
PHOTOS:
Illustrated below: Walking toward an oblique edge "in step" and "out of step." In both instances, the cane movement is the same – at the first step, the cane is near the edge, then the cane is moved to the left away from the edge, and the third and last step the cane goes to the left over the edge.
Walking "in step:" When the cane is on the user's right (near the edge) the user's forward foot is on the left. At the second step, the cane is on the user's left and her forward foot is her right foot. The last step, the cane goes over the edge at the same time that her left foot steps forward, safely on the platform.
Walking "out of step:" When the cane is on the user's right (near the edge), the user's forward foot is also on her right. At the second step, the cane and the forward foot are both on the user's left (away from the edge). The last step, the cane and her foot both go over the edge together, with no warning.
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