The Falling Men (砂飛行, Sand Flight, comparable to Takofuusen's filename) are tiny, decorative stick-figure characters that appear randomly in the background of the Stairway to the Sky in their own event.
Overview
The Falling Men will appear as Madotsuki walks up the Stairway to the Sky, falling in the background. As they are decorative characters, they can not be interacted with and do not react to any effects. When the player walks across two tiles along the stairs, a 1/4 chance is triggered for each one, although the second one can only show up if the first one did, making the second one very rare to encounter, being a 1/16 chance.
Speculation
Considering the Falling Men appear around a large pyramid, it may also relate to the presence of indigenous imagery found throughout the game, particularly Aztec imagery. The Aztecs are commonly associated with their religious rituals which took place at the tops of pyramid-like temples serving as places of worship. Human and animal sacrifice was occasionally a part of these rituals, and humans who were used for such events were typically tumbled down the pyramids after being properly sacrificed, as shown in various pieces of Aztec art.
Some fans have speculated that these characters could be foreshadowing the ending of the game, showing that even in her dreams, Madotsuki is thinking about killing herself. Some other aspects of the game's world may allude to the ending, such as the shoes on Madotsuki's balcony (as taking your shoes off before committing suicide is customary in Japan) and the Witch's Flight event, which can be quickly canceled to make Madotsuki fall from the sky.
Spoilers end here.
Gallery
Closeup of their in-game sprite
Two falling men
