The Falling Men (砂飛行, Sand Flight, comparable to Takofuusen's filename) are tiny stick-figure decorative characters that appear randomly in the background of the Stairway to the Sky in their own event. They appear as the player walks up the steps towards the top and cannot be interacted with in any way.
The Falling Men are simply drawn stick-figures that spiral around in the sky (like the UFOs and Severed Heads), although they never reach the ground themselves. 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.
Their in-game sprite.
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 things that could be possibly foreshadowing the ending is the fact that there are shoes on the balcony, as taking your shoes off before committing suicide is customary in Japan (which already has high rates of suicide), and the eggplants in NASU, both of which are seen from the start.