Final answer:
The hair layer consisting of unique protein structures that give hair most of its pigment and strength is known as the cortex. It's a middle layer that determines hair texture and color, and it surrounds the medulla in some hairs.
Step-by-step explanation:
The layer of hair consisting of unique protein structures that give the hair most of its pigment and strength (elasticity) is called the cortex. The cortex is the second or middle layer of keratinocytes originating from the hair matrix, encased by the outermost layer called the cuticle and, in some hairs, surrounds the medulla which is the central core. Hair texture and color are largely determined by the shape and structure of the cortex. The hair itself is a keratinous filament growing out of the epidermis, composed of dead, keratinized cells which explains why haircuts are painless as the external hair does not have sensation.