Should I Kill Jeremiah Compson?

While there's no prompt to do so, it's heavily implied that you can decide to kill Compson or leave him in all his misery to rot. The choice is up to you, but killing him does grant you additional honor. If you shoot him while he's on his knees, he'll fall into the fire and burn.

What did Jeremiah Compson do?

Events of Red Dead Redemption 2

During the search, the player discovers that Compson was once a slave catcher by the notes in his ledger, often writing how proud he was of the work he did in the position. ... The player then throws his possessions into his campfire, causing Compson to cry and fire the pistol at the player.

How do you tire out Jeremiah?

Empty Out Stamina Bar To Tire Jeremiah

To tire Jeremiah out, you need to run his stamina bar dry. You can do this by running in the fields around the ranch & repeatedly pressing the gallop button.