What is the term for the condition where the skin around the nail plate is living skin that is torn?

The term that describes the condition where the skin around the nail plate is living skin that is torn is indeed hangnail. Hangnails occur when a small piece of skin along the edge of a fingernail or toenail tears or separates from the surrounding skin. This often results in a painful and sometimes infected area. Proper care, such as moisturizing the cuticles and avoiding biting or pulling at the skin, can help prevent hangnails from occurring.

In contrast, nail pterygium refers to a situation where the skin grows over the nail bed, which is not a tearing condition. Plicatured nails denote a nail deformity where the nails curve downward due to the folding of the nail plate, and koilonychia, often known as spoon nails, is a condition where the nails have a concave shape. Each of these terms denotes a different condition than what is described, thereby reinforcing why hangnail is the correct choice.