After Mayor Richard's trust is earned, he informs the Initiate about the whereabouts of the Paladins: They entered the Carbon Crater. After receiving the Elevator Key, the player has to search the crater to find the Brotherhood. Once they reach the bottom of the crater, the Initiate realizes that the information provided by the Mayor is false.
Mayor Richard waits for the player along with several raiders, angry for the death of their friends. The raiders forced him to cooperate and set the player up, as otherwise they'd burn Carbon down to the ground. The player has to kill the Mayor to proceed.
He is a predictable foe, throwing out several (3-4) grenades before moving to another location in the cave. Richard is immune to his grenades, but the raiders accompanying him are not. The Mayor will typically kill off the raiders or heavily wound them at minimum. Regardless, the raiders aren't much of a threat, as they are primarily equipped with melee weapons, with only a few wielding guns.
The quest is completed once Richard is dead.
Inside the cave are numerous cases of ammunition and a quantity of stimpaks, scattered in the three corners of the cave.