Caesar's Foe is the name given in the G.E.C.K. editor to the quest which controls the appearance of legionary assassins. Should the Courier's negative reputation with Caesar's Legion reach a certain point, legionary assassins will be dispatched to kill them. As of patch 22.214.171.124xx, this quest has been dismantled and replaced with "Faction Hit-Squad Master Quest," with the same in-game function.
Legionary assassins are dispatched within hours of the Courier first attaining a sufficiently negative status with the Legion. Thereafter, assassins are dispatched approximately every three days, depending on whether or not the Courier is located in an area where they can be attacked.
Previously, this quest would only cause legionary assassins to appear once. Due to scripting errors, any further appearances of legionary assassins would not be triggered, regardless of the Courier's location or reputation with the Legion. This issue has been fixed as of patch 126.96.36.199xx. [verified]
If Boone is not a companion, wearing Legion faction armor before the assassins are able to see the player character will result in the decanus engaging in dialogue with the Courier, saying that they are marked for death. As soon as the dialogue ends, the hit squad will stay still, allowing the player character to kill them one at a time with melee sneak attacks, given the player character can kill the assassins with one sneak hit. [verified]