I'd guess that it a "no slip" inner waistband designed to keep the jersey tucked and the reason Briscoe's is visible is because I think he rolls the waistband over to achieve his short(er) shorts look. The drawstring is usually visible on his britches too.
I don't have any idea what it is but tonight is the first time I've seen them. Tyler has one on and I saw Willis had one on too. Shiny and black around the waist. I'm clueless.
It's just the inside of the shorts' waistband. Ulis and briscoe role their shorts over: Ulis because he's tiny, Briscoe because he likes rocking the short shorts.