From the Super Mario Wiki
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Paper Luigi is a paper incarnation of Luigi based on his appearance in the Paper Mario series that came out of a magical book in Mario & Luigi: Paper Jam. Paper Luigi is an independent character from Luigi and appears only after the player unlocks the Music Player after beating Shiny RoboBowser. He appears to sleep in Twinsy Tropics while Mario, Luigi, and Paper Mario are on their adventure.
Paper Luigi was planned to be playable in Mario & Luigi: Paper Jam but was taken out because it would be too difficult to control four separate characters.