cord, woven belt, hem, hemming
緄 centers on a textile edge or binding: a cord, woven belt, hem, or the act of hemming. The common thread is a narrow fabric strip used to finish or secure an edge.
緄 combines 糸 (thread) with 昆, which likely provides the sound. The character originally referred to a woven cord or belt, fitting the thread component.
The left side 糸 is thread, and the right side 昆 looks like a comparison of two things side by side. Imagine thread being compared and woven into a cord or belt, or used to hem an edge.
For コン, picture a con artist weaving a cord belt as part of a scam: con -> コン, and the thread 糸 is being twisted into a cord.