Shivering:Final Resting

Quick Walkthrough
# Hear rumors around Crucible about Hirrus Clutumnus.
# Talk to Hirrus Clutumnus.
# Meet him by the sewer grate at night and hear his proposition.
# Put him out of his misery.

Detailed Walkthrough
Meeting Him
Hirrus Clutumnus wants to die, according to the citizens of Crucible.  He has lately taken to asking random people for their help with the twisted matter; locate him to see if the rumors are true.  You can find Hirrus Clutumnus walking around town.  Talking to him results in his asking you to meet him after dark by the sewer grate northeast of the large statue of Sheogorath that adorns the entrance to Crucible (at the south end of Crucible, southeast of Sickly Bernice's Taphouse).

A Quick Chat
When you meet Hirrus near the grate, he tells you that he is miserable and wants to die.  But he doesn't want to be the one to do it, because then he would end up like the poor souls on the Hill of Suicides, who endure an unhappy purgatory for eternity. Hirrus wants you to do the deed for him, but he doesn't want you to just outright attack him. He would like it to be a surprise, so that his last moments aren't totally terrifying.  If he sees you after talking to him at the sewer grate he will say, "Stop! Take me unaware, not like this!" and flee, obviously not wanting a painful death.  In fact, immediately after you finish your conversation outside the sewer grate, he will often cower in fear. It is easy to erroneously assume that this is your cue to kill him; don't, as there is a Dark Seducer posted right there at all times. Just walk away and wait for a better chance.

Assist and Descend
Making it easy, Hirrus climbs the stairs near the palace in the evening and conveniently stands right at the top of a long drop, enjoying the view.  If you choose to talk to him you are given an option to push him off the ledge to a swift death. You do not get a bounty if you kill him this way, and the nearby Dark Seducer standing on guard will say (in a seemingly gleeful tone), "Someone really ought to put up a railing.  That happens all the time." Hirrus' final words before falling to his death are, "Peace at last. Thank you! Thank you..."  Another option while he is on the ledge is to walk into him repeatedly until you nudge him off the edge, which will also count as a surprise and an accident.

It is also very easy to follow Hirrus and sneak attack him. If you have a high enough sneak rating, the attack should kill him in one blow, giving a quick and easy end to the quest and Hirrus' life.  Be careful if you kill him this way, because you are likely to incur a bounty from the Dark Seducer guards. If you entered the Shivering Isles through the Mania Gate, then you can use the Blessing of Mania spell to provoke him into attacking an NPC such as a guard, which will result in his death.

You can also cast a frenzy spell on the nearby guard who will kill him and this will count as a surprise kill

If you kill him as requested, without him knowing he was about to die, you will find a key to his house on his body.  Upstairs in the house is a jewelry box with a leveled Ring of Happiness, which counts as your reward and officially completes the quest.  The ring is enchanted with Feather, Light, Water Walking, and Fortify Personality enchantments.  In the jewelry box you will also find ''Hirrus Clutumnus's Will'', which explains that he tried wearing the Ring of Happiness for a while, but it made him "feel odd - not myself".

Notes
Evidence of previous citizens falling to their deaths can be seen in the sewage ravine below the platform.  There are a few scattered bones, rib cages, and pools of blood lying in the general vicinity of the drop.
A tombstone will appear after Hirrus' death in the New Sheoth Graveyard. Activate the tombstone to read his epitaph: "Hirrus Clutumnus never felt like he fit in anywhere. He fits in a coffin quite nicely, now."
The containers in Hirrus' house, including the jewelry box where you find the Ring of Happiness, are non-respawning containers and can be used to safely store items.
If you jump off the ledge after Hirrus, when you loot his corpse, the key may not yet be present.  Wait for the quest message to appear, then loot his corpse again to get the key.

Bugs
 
It is possible to take him to the sewer grate with a strong Command Humanoid spell, once the spell wears off talk to him and the quest should continue normally. You may need to push him a little bit so he stands close enough to the grate.
 
 

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