Final answer:
Elastin is the protein fiber found in the dermis of the skin, providing it with flexibility and the ability to return to its original shape after being stretched.
Step-by-step explanation:
The protein fiber found in the dermis that is responsible for giving skin its flexibility and firmness is elastin. Collagen fibers in the dermis provide toughness, while elastin fibers give the skin its elastic quality, allowing it to stretch and then return to its original shape. Besides these fibers, the dermal matrix also includes other proteins that contribute to the strength and flexibility of the skin.