It’s dead skinny! (7)

I believe the answer is:

cuticle

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If this is the answer I cannot explain how the clue works.

(Other definitions for cuticle that I've seen before include "finger has one" , "Dead skin on hand" , "Dead skin at the base of a fingernail" , "Dead skin at nail's base" , "Skin around the nail" .)

I've seen this clue in the Evening Standard.

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