Final answer:
The loose and pliable overlapping skin around the nail is the cuticle, which serves as a protective barrier for the nail plate. Therefore, the correct option is 3).
Step-by-step explanation:
The loose and pliable overlapping skin around the nail is the cuticle, also known as the eponychium. This fold of epithelium extends over the nail bed and is a key component of nail anatomy. It helps to seal the edges of the nail plate, preventing infection of the underlying tissues. The nail plate is the visible keratinous part of the nail, whereas the nail fold is the groove in the skin in which the nail plate is embedded, helping to hold it in place.