In Brawl, this was a tether recovery where Olimar would use whatever Pikmin he had with him to grapple to a ledge, something made up entirely for Smash.

Smash 4 onwards, however, introduced the Winged Pikmin from Pikmin 3 which will carry Olimar and however many Pikmin he has with him back to the stage.

While there's never a point where you use the Winged Pikmin for this purpose, there is a section of Pikmin 3 where they can carry an unconscious Olimar, so... close enough!