The Oubliette is the Virindi's disposal site for "non-viable" test subjects.
Walk Through
Once you have entered the dungeon, head north through the large room ignoring the side passages and jump into the pit.
From here, go south through the corridors until the walls and ceiling look different and then make your way around and down either of the ramps heading north.
Here you will find a pit with a very long drop. At the bottom is the The Gibbering.
Make sure you're buffed before jumping down. It debuffs your attributes as well as vulning you for armor and bludgeoning using level 7 spells.
During the The Risen Princess event the way the Oubliette Quest resets was addressed to avoid encountering possible ways to get stuck with extra long reset timers.