The half-box is a short men's haircut with a gradual taper in length (from 3 to 8 cm on top, tapering to shorter at the temples and the back of the head). Unlike the classic «box» cut, it allowed for bangs and less abrupt boundaries between zones.
Historical context
By 1993, the «half-box» was seen as outdated, a «Soviet-issue» style — worn mostly by military men, police officers, and the older generation. Young people preferred Western-style looks: the «Canadian» (shaved temples), the undercut, or long hair «a la Kurt Cobain».
Criminal subtext
In criminal slang, the phrase «shear someone down to a half-box» meant not just an actual haircut (say, in prison), but also, metaphorically, to «fleece» a victim. In this context, Zhorik is hinting at the systematic bleeding of money out of Sergei — like carefully shearing off hair zone by zone.
Interesting fact: in the 2000s the «half-box» evolved into modern variations of the «crop» with fade elements, and in the 2010s it became associated with subcultures — from hipsters to neo-Nazis.