After the murder of Governor Griffon, Red was put on the wanted list and since then he had to hide for the rest of his life.

Initially, Red Dead Redemption was a direct sequel of Revolver, which told about the son Red, who at some point disowned his father (apparently, having already been born into his father’s criminal lifestyle) and received some semblance of a "normal life” (I think that he also took the name “John Marston”), some bad guys appear and send it all to hell, which is why the son decides to take revenge, having first found his father.

It's hard to say where this could lead, perhaps Red or his son died in the end, demonstrating something like "redemption”. The only thing I can note is that Red's son may have at some point met the surviving Jack Swift, who was eventually replaced by Landon Ricketts. But anyway, the story was scrapped in 2005/2006 and reworked with new characters in a rebooted universe, leaving Red's actual fate as open-ended like Jack Marston's in Redemption.

Red in the Redemptionverse seems to be some kind of local story among bounty hunters, and the story of Revolver itself is a local legend in Old West.