I was able to break the Faceless barricade using AoE Enrage, a 729 capacity high frequency shield, abusing zone transitions to heal/save/recharge, and using adrenaline/morphine before entering. However, they seemed to keep coming as I killed them. I got especially suspicious when I saw a couple coming from the drill area late into the fight.
Do the Faceless at the barricade keep respawning, or can you actually free Core City from them? Even if not, is there anything good to loot if you somehow keep them all occupied?