Red Dead Redemption 2 is a savage world, where people can easily find their fortune as easily as they can lose everything. The latter is definitely the case of Jeremiah Compson, main character of The Iniquities of History Stranger Mission.
To begin The Iniquities of History Stranger Mission, you need to speak with the man sitting on the bench in front of the Rhodes' Train Station at any time from Chapter 3 onward. The man, visibly drunk, is named Jeremiah Compson, and he will tell Arthur that he has lost some important things that cannot be restored to him, like his house, valuables, and honor.
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Some of the valuables, however, can be recovered and he asks Arthur for help in doing so. Never one to leave others in need, Arthur accepts to bring back a watch, a pistol and a ledger, which are all located at the man's house.
Once you are doing talking with the man, the location of his house will be marked on the map. It's actually pretty close to Rhodes, so it won't take long for you to reach it. Once inside the house, you can start searching for the items Jeremiah asked Arthur to bring back.
The first item is the watch, which can be found on the chimney of the first big room encountered after entering the house. Use Eagle Eye to mark points of interests that may lead you to locate the remaining items. Interact with the picture found on another chimney in the house to reveal that there is a hidden trap door nearby.
At this point, Arthur will make the acquaintance of some squatters who have settled themselves in the abandoned house. One of them is using the gun Jeremiah asked you to bring back. Once the talking is done, you will have to deal with them, you can either use the knife or switch weapon and kill them easily. After the squatters have been dealt with, you can pick up the gun.
The last item to recover is the ledger, which can be found in the basement. To reach it, interact with the trap door that has been discovered earlier. The ledger is found on a crate on the right sight of the basement. Taking a look at the ledger makes Arthur understand that Jeremiah is far from being the decent and honorable man he thought he was dealing with.
Now that the three items have been recovered, it's time to get back to Jeremiah. He can be found in the marked location on the map.
The confrontation, obviously, doesn't go too well. Arthur will show his disappointment at the man, and in turn Jeremiah will show that he feels no remorse for what he has done in his life. Arthur eventually throws the ledger into the fire and Jeremiah will be on his knees.
At this point, the mission is over, but there is still something you can do. If you kill Jeremiah, your Honor rating will increase. It also feels like the right thing to do, considering how much suffering he brought to others.