One of Skyrim's mystery. Narfi is a beggar who lives in the ruins of his family home in Ivarstead. He's insane and rumble about his missing sister, the same you can find by doing your own investigation - Well, her skeleton. Interesting thing, Narfi is a quest giver since he's the one asking for the investigation (The Straw that Broke) but also the target if you're a member of the Dark Brotherhood (Contract: Kill Narfi). Sounds unusual? What happened to her and why is Narfi a potential kill for the DB? I've listed some theories, facts and thoughts.
City guards, bandits or hunters?
If you did the quest you know that Reyda is underwater, near the bridge. All that's left of her body is her skeleton and some loot : her necklace (let's keep that one for later) and random alchemical ingredients in a satchel, always rare as far as I'm concern. Now, near her you can also find is some stray arrows so it's easy to think she may have been shot picking ingredients, accidentally or not. After all, you meet some hunters yourself in your way to High Hrothgar. See, I don't like this theory for two reasons : first she's appearently gone for at least a year. I don't think arrows can stay in the same place that long, at least in water. There's wind, rain, etc that move things or even the river itself. I don't know if I'm the only one and my game is bugged but I don't always find these arrows. And I always look for them when I decide to do the quest.
Near Riften are Geirmund's Hall and Shroud Hearth Barrow, both are Nordic tombs and dungeons you can explore. Shroud Heart Barrow in particular, is a place that worries the inhabitants since they think the tomb is haunted (and they're right about that). You get Lifting the Shroud, a request from the innkeeper Wilhelm to investigate the place. As for Geirmund's Hall it's a bit far and resting place of Sidgis Gauldurson. I'd say the first one is a possibility : same scenario, the lady is picking ingredidents and she got attacked but it's a bit far from the river.
My personal pick. When Narfi gives you the quest, he mentions that the innkeeper said that Reyda would come back. Wilhelm is the only person in Ivarstead who mentions Reyda or even Narfi who is very much alive but ignored by the inhabitants. I find that curious. Wilhelm is the one who point you in the direction of a small island saying that she was there and what she was doing, even more curious. Remember the necklace? you're supposed to bring it back to Narfi, but if you return to the innkeeper instead there's a bug and he answer with words that are supposed to be Narfi's : "Reyda! You saw Reyda? Did you tell her Narfi cries? Did you tell her Narfi never said goodbye like mother and father?" and suddenly leaves the dialogue box. Why is this bug here? Because obviously Wilhelm was supposed to react to the necklace. The line "I tried to look for her, but she never turned up" implies that Wilhelm seems to have a personal interest in her. So my guess is that Wilhelm may be the killer and he tell the beggar that his sister will come back because he's ashamed. An accident, maybe?
I think it's the most popular one because there's visible clues and many reasons we sould consider it seriously. Let's start with the line "With father I said goodbye... with mother I said goodbye. Reyda leaves and Narfi can't say goodbye". Two things : he seems to know for sure that she's no more and we know his parents are dead but not how. The ruins where he lives seems burned so maybe he killed his parents in an act of madness and did it again with Reyda. Maybe it was actually accidental but he started to become insane and pushed his sister in the river later.
Another theory I've heard about Narfi is that he may be a werewolf: In the poem Lokasenna from the Poetic Edda, Narfi is one of Loki's son and can turn to a wolf. Our Narfi says "If you see Reyda, tell her that Narfi misses her and to come home soon... very soon. Soon... soon, like the moon!". Also, if you kill him you can occasionally loot human flesh and human heart. Remember the werewolf Sinding from the Daedric quest Ill Met by Moonlight? Maybe that's the explanation for the beggar's insanity and loss. If he's really a werewolf his lycanthropy is probably unstable and he's more or less oblivious. Just Imagine : your sister is peacefully collecting ingredients, you suddenly transform and when you come back there's nobody around. Worse, your sister is now underwater and so close to you but you can't remember... My problem with that theory is that we don't loot a pelt when we kill him, and I think we usually do when we kill a werewolf. Also, if I pick the werewolf form city guards joke about fur in my ears and complain about the howling in Jorrvaskr but here in the middle of nowhere they failed to notice it?
To be frank, we're in Skyrim. It means that we may theorize during hours about nothing but an unfortunate tumble or a blank from the writers. We may never know.
One last thing : Why the contract on Narfi's head? Who wants him dead?
I know some people think that it's about his plot of land but I don't think that. It may be because he's a murderer but I think it's about pity. Wilhelm may be the one, because there's nobody to keep an eye on Narfi anymore or because the beggar started to ask some Dragonborn to search for Reyda. Maybe it's the town, silent about him but still seeing him. Or maybe it's the first and/or the second because he's indeed a werewolf and he's dangerous. Nazir has contracts about all sorts of people but you have to admit this one is a strange one.
What about you? What do you think happened? Do you see other clues I forgot to mention?