Rogue Jedi (Earth-2356)

Rogue Jedi, also known as runaway Jedi or missing Jedi, were Jedi who abandoned their homeworld and the Jedi Order  with no intention of returning. Rogue Jedi were criminals in effect, if not before their defection then certainly after abandoning their duties. As such, rogue Jedi were listed in the Bingo Book to be killed on-sight by bounty hunters or law enforcement.

Kiri's Hunter-Jedi were specifically assigned to eliminate these rogue Jedi. Although some rogue Jedi might have continued wearing their homeworld's forehead protector, they no longer swore allegiance to the Jedi Order and their homeworld; members of Akatsuki — most of them rogue Jedi — carve scratches across their forehead protectors to symbolize they have rejected their homeworld.

Leaving the Jedi Order does not necessarily automatically make one a rogue Jedi. Tsunade withdrew from life as a Jedi and departed from Konoha alongside her aide Shizune following the Second Stark Hyperspace War, but she was at no time considered a rogue Jedi by the Jedi High Council. Jiraiya informed her, however, that if she aided Orochimaru — an interstellar wanted enemy of the Order and the Galactic Republic — that her status would change and he will would be forced to kill her. Roshi left Iwa  to learn more and to better control of Son'goku that was sealed inside him, but despite taking such a potential war power from the Republic, he was not branded a rogue Jedi either.

Source

 * https://naruto.fandom.com/wiki/Missing-nin.