After the fight among the Orcs, Shagrat (in both the book and film) smuggled the shirt past Sam Gamgee and delivered it to the Dark Tower.
Steve Peregrin Took was credited as "Shagrat The Vagrant" on Mick Farren's 1970 solo album Mona - The Carnivorous Circus and the two formed a band called Shagrat, also featuring guitarist Larry Wallis.