This mystery can be found in the east of Jotunheim, north of Ymir’s Altar. When you approach the Jotnar by the cage you’ll hear her pleading to her lover, who has been locked within it. Speak with the Jotnar to learn more about the situation.
After speaking with the Jotnar woman, make your way to the northern side of the house, where you’ll find a locked door with an exposed link to break the lock. Destroy the link by hitting it with a basic melee attack or shooting it, then enter through the door. As soon as you enter you’ll find that the door was an illusion, with no inside to the house on the other side. However, if you turn around you’ll find that the rest of the house is revealed.
Once you’re inside the house properly, inspect the comb on the table to prompt a comment from Havi. You’ll also find a note on a barrel in the north of the house, providing more context with regard to why the man outside might have been locked in the cage, and a wealth chest to the east, which contains an Ymir’s Tear Stone. Once you’ve inspected the note and looted the chest, make your way back to the door from which you entered.
When you reach the door (or begin to walk up the stairs), you’ll be spotted by a Jotnar Cutthroat. You’ll need to fight him until he’s down to around a quarter of his health. At this point you can speak with him and decide whether to fight him to the death and take the key, demand that he give you the key in exchange for his life, or tell him that he’s been wronged, and so you’ll spare his life and allow him to keep the key.
If you want the best outcome for the two Jotnar outside, we recommend fighting the Cutthroat to the death and taking the key from his corpse. We think this is justified, since the Cutthroat is planning to beat his wife and kill the Jotnar he’s imprisoned, and we don’t think the note on the barrel reveals the full truth of the tale. If you choose not to kill him, you can still take the key from him and free the Jotnar outside, but neither will be able to inherit the house, which they claim is rightfully theirs.
Whatever your decision, once you’ve dealt with the Cutthroat and spoken with the Jotnar outside, the mystery will complete.