The Fallen Monks are enemies in Final Fantasy X. They are the unsent remnants of the old Warrior Monks killed when Sin destroyed Zanarkand one thousand years ago. They share the same stats, but have slightly different appearances and wield different weapons. The first wields a rifle, which damages one enemy and may cause the Zombie status, and the other a flamethrower, which inflicts Fire damage on all characters. The two are in permanent Zombie status, thus, restorative attacks damage them. An easy way to defeat them is to use reviving items or magic, such as Mega Phoenix.
Both types of Fallen Monks, as well as both types of Warrior Monks, count as two enemies for the purpose of anything that counts kills (such as Karma damage or the Slayer overdrive mode). This is because their weapon is considered a separate (albeit untargetable) enemy.