This is a unique quest that can only be accessed by using a Oubliette portal gem found on Virindi Consuls and Virindi Adjudicators. It gives you access to the Virindi's disposal site for "non-viable" test subjects...
Walk Through
Once you have the portal gem make sure you you buff fully as you will fight Virindi Adjudicators, Consuls, Ascendant Drudges and Tusker Assailers almost immediately.
Head north ignoring the side passages through the large room and jump into the pit.
From here go south through the corridors fighting Tusker Assailers, Devastators, Drudge Bloodletters and Virindi Consuls.
You should notice a change in terrain and Peerless and Cabalist Drudges will appear.
Make your way around and down either of the ramps north.
Here you will find a pit with a very long drop, at the bottom of which is The Gibbering.
Make sure you're buffed before jumping down. He debuffs your strength, coordination, quickness, focus and self as well as vulning you for armor and bludgeoning using level 7 spells.
Once you have defeated him take the Gibbering Claw. There is also a unlocked Runed Chest here with tier 4/5 loot.