612. A Broken Fastener
84:16 One may go out wearing a tallis with tzitzis in the usual manner. One may not wrap the tallis around his neck in a place where it is not normally worn in this fashion.
84:17 A garment that is closed with two straps or laces, or that has clasps, if one of them is broken, the remaining one is no longer considered significant. Nevertheless, if he intends to mend the broken fastener after Shabbos, then the remaining one is not considered insignificant. Therefore, wearing the remaining fastener outside would be considered carrying a burden and prohibited. If one does not intend to fix the broken fastener, then since the remaining one is not considered significant, it is subordinate to the garment and one may go out wearing it. If it's valuable, like a silk strap or a silver clasp, then it is not considered subordinate even if he doesn't intend to fix it and one may not go out wearing it on Shabbos.