black, police runners (from the black clothes formerly worn by them)
皁 centers on the color black, specifically the black clothing once worn by police runners, giving it a secondary association with those officials.
The origin of 皁 is uncertain. It combines 白 (white) and 十 (ten), but the historical reason for this composition is not clearly established.
Picture a white 白 uniform with a black 十 mark on it, like the black clothes once worn by police runners. The black mark turns the white into black.
For ソウ, imagine a police runner in black clothes sewing a black patch: sew -> ソウ, and the black thread matches the black uniform.