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Background
Starting on Day 2, you can meet a working class woman in front of the
Doomed Commercial Area (#1). Even though she'll deny it, you can insist that her husband is missing, and that you should open a Missing Persons case. Afterwards, if you approach the drunk to the south (#2) while having at least 2 Authority, a thought orb should appear over your head. When you click on it, you'll decide that the drunk must be the missing husband.
When you point out the drunk to the woman, she won't recognize him, but she'll finally reveal that she hasn't seen her husband since he left for the library the day before, and that he's wandered off before. She'll then give you a description of him -- chubby, alcoholic, wearing a brown coat with a blue lining -- and she'll ask you to find him. This will trigger the task.
Walkthrough
You'll find the corpse of the husband on the boardwalk in
Martinaise West (#3). When you examine him, you'll find a
Folded Library Card in his pocket, and you'll deduce that he died when he fell through a weak board in the boardwalk and hit his head on a nearby metal bench. You'll also recognize him from his wife's description, which will complete the task and earn you 30 xp.
After you've completed your examination of the corpse, you'll be given two options: to identify the man yourself or to let Kim's precinct handle it. This will trigger one of two tasks:
Dead Body on the Boardwalk or
Report the Dead Body to the Station. If you want to return to the working class woman and let her know what happened to her husband, then you should choose the first option.
Note: If you find the husband before triggering this task, then you won't be able to trigger it.
Another Note: If you examine the corpse without Kim, then you'll trigger the task
Return to the Dead Body with Kim. You'll have to complete that task before you can complete this one and decide who should identify the corpse.
1 - Working Class Woman
2 - Drunk
3 - Corpse