If Jigglypuff uses Sing on this stage while the screen in the background of Pokemon Stadium is focused around it, all three of the other Jigglypuff on the ground will fall asleep, and for much longer than they usually would. This easter egg is known as sleepy time. The effect is not unlike Peach Blossom, Peach's Final Smash in Brawl.
It is possible that the number of this event refers to Jigglypuff's number in the National Dex in the Pokémon games: #039.