The quality of being flexible, either literally or figuratively, is pliability. The pliability of aluminum foil is what makes it such a great material for wrapping your leftovers — or fashioning a crown for your cat.
Clay's pliability is what makes it moldable. This word comes from the French pliable, "to bend," and a Latin root meaning "to fold." Anything you can bend, fold, twist or turn without breaking it has this quality of pliability. Figuratively, pliability refers to someone who's easy to "bend" or influence: "The pliability of those kids meant they'd believe anything they read online."