Elasticity should not be confused with plasticity. The return to the initial state is elasticity. The deformation that remains permanent is plasticity.
The opposite of elasticity is plasticity; when something is stretched, and it stays stretched, the material is said to be plastic. When energy goes into changing the shape of some material and it stays changed, that is said to be plastic deformation. Creep is the deformation of a material due to sustained stress or load.