"It means one of them is lying..." This article or section of the article is non-canon. All information listed below that regards to storyline and plot are not considered a part of the main canon timeline.
The objective is for Cole to escort the prisoners to a fixed location. Along the way, the prisoners will attempt to flee or attack Cole, and he must shock them until they submit and resume walking. He can zap a prisoner during the march to make them walk faster.
In the Warren, Cole escorts four standard Dust Men held captive by Reaper Conduits. In the Historic District, the only the prisoners Cole will escort are three First Sons conduits.