The most insane flexible screen proposal from Nokia was the "nanotech" one - Nokia Morph [1], where the phone "normal" candybar shape was formed out of folding it twice with a clip for speakers - you would pull the clip and unfold it into something akin to A5 or A4 paper. Future sounded bright with software defined tactile buttons and the like.

[1] https://www.youtube.com/watch?v=IX-gTobCJHs

Looks amazing! And absolutely reminded of this scene from Silicon Valley: https://www.youtube.com/watch?v=CFsRif1wVGs