Final answer:
The rubbery protein fiber called elastin is abundant in elastic fibers which allow tissues to stretch and recoil, such as in the skin and ligaments of the vertebral column. Elastin, combined with collagen in dense connective tissue, enables flexibility and resilience in body structures.
Step-by-step explanation:
The rubbery protein fiber most plentiful in tissues that require the ability to stretch and then recoil is called elastin. This protein is a key component of elastic fibers, which have the unique property of being able to return to their original shape after being stretched or compressed. Elastic fibers are found in many body tissues including the skin and the elastic ligaments of the vertebral column.
One notable example of where elastin is found is within dense connective tissue, particularly dense regular elastic tissue which contains elastin fibers in addition to collagen fibers. This combination allows structures like ligaments, including those in the vocal folds and between the vertebrae, to return to their original length after being stretched. The presence of elastin provides flexibility and resilience to the tissues it inhabits, an essential property for the proper functioning of various organ systems such as the lungs, large arteries, the bladder, and elastic ligaments.