bottom of the sleeve
Archaic term for the lower edge or opening of a sleeve.
In old texts, there are descriptions of mending the frayed bottom of a sleeve.
height of the sleeve (of traditional Japanese clothing)
Refers to the vertical length of a sleeve in traditional garments like kimono.
When measuring the sleeve height of a kimono, you check the length from the shoulder to the cuff.
袖下 is sometimes used to mean a secret bribe, but it is rarely seen in modern Japanese.
Compound of 袖 (sleeve) and 下 (under/bottom). The bribe sense likely derives from the image of hiding something under a sleeve.