With Falcon and the Winter Soldier coming out on Disney+, Amazon Prime Reading had a bunch of the comics featuring those characters for free, so I wound up reading them. That was the inspiration for the question in the title: what do you do with a replacement hero once they've been replaced--by the original hero, usually.
After the Civil War event around 2007, Steve Rogers was shot and killed by an assassin. His former sidekick Bucky Barnes, most recently the assassin known as the Winter Soldier, took over as Captain America for a little while. Until Steve of course came back--for a few years.
Then around 2013 or so, a villain sucked the super-soldier serum out of Steve's body so he got old and weak. This time Sam Wilson, aka The Falcon, took over for him for a couple of years. Then Steve came back and there were two Captain Americas. But that Steve was an evil double created by a Cosmic Cube or something. A second, good Steve, came back in the Secret Empire event of 2017 or so, during which Sam stepped down as Captain America.
So what became of Bucky after his turn as Captain America?
In a series immediately after that, he and Black Widow go after some former Soviet agents who were involved in the Winter Soldier program. I read the first volume and it was pretty good. More in that down-to-earth thriller vein of the Disney+ show.
That series ended after a couple years. Then in the Original Sin event (about the same time Sam Wilson was taking over as Cap) it's revealed that Nick Fury has for decades been secretly protecting Earth from threats in space and whatnot. When he dies, Bucky takes up the mantle.
I read the first volume of the new series with Bucky and Maria Hill out in space. It was obviously a lot less down-to-earth and the art was the cruder type I don't really like. So overall I didn't think much of it. And neither did most people because I think it had only two volumes or about 12 issues before it ended.
The last one I read was from 2018 or so. Bucky has returned to Earth and with Sharon Carter set up shop in Indiana as kind of an independent Witness Protection Agency. It's kind of like the Schwarzenegger movie Eraser from the mid-90s where his job was to rescue witnesses in distress and get them set up with new identities. Trying to save one guy, Bucky meets a kid who has been trained to be an assassin from a young age and so Bucky takes him under his wing as sort of a sidekick. It was better than the space series but not really as good as the first one and I don't think it lasted all that long. Again, probably about 12 issues.
What about Sam Wilson, the Falcon?
I read the 8-issue 2017 series after he stopped being Captain America. It was pretty underwhelming. At the start Sam and a teenage SHIELD agent calling himself Patriot go to Chicago to stop gang violence. So this is going to try to be a down-to-earth, socially relevant series? Um, no. The mayor of the city is actually Blackheart, the son of Mephisto, the devil of the Marvel universe. Blackheart gives one of the gang leaders some magic to set off violence all through the city, which Sam and Patriot have to try to stop. This involves Sam actually going to Hell before he can escape.
The last three issues go back to New York, where Mephisto sics vampires on Sam, Patriot, and Misty Knight. With Blade's help they're able to stop them. Hooray! There's a really rushed, unsatisfying romantic plot with Sam and Misty.
This series is really what made me think about this subject because it seemed like the author was struggling to find something for Sam to do. That is pretty much always a problem for these characters. After you've had them be a big-time hero like Captain America, Batman, or Superman, where do you go from there? It's a tough act to follow.
In the 90s DC replaced both Batman and Superman for a little while. After Superman "died" there were four replacement heroes: Steel, Superboy, Eradicator, and Cyborg Superman. The first two remained heroes wile the Eradicator pretty much disappeared and the Cyborg Superman became a villain. Steel had his own comic for a little while and a crappy Shaquille O'Neal movie. That Superboy stuck around for a little while too but was eventually replaced by the more popular Connor Kent version in Young Justice and the Titans TV show. Steel still shows up in Superman and other DC titles and I think is in that Superman and Lois show on the CW though I don't think he's a hero yet.
In 1993-1994 during the "Knightfall" event Jean-Paul Valley, aka Azrael, took over for Bruce Wayne after Bane broke him. Exposure to Scarecrow fear gas made Jean-Paul crazy, paranoid, and brutal and eventually Bruce took back the mantle. After that Azrael had his own series of 100 issues before he was killed off. Having read that series, it was obvious author Denny O'Neil was struggling to establish a new identity for Azrael. Sometimes he was traveling the globe. Sometimes he was in Gotham. A few issues he was in a smaller city. He went through a few costume changes too. Nothing really worked. The character was brought back in the post-Rebirth Detective Comics but really just as a minor part of the "Bat Family." He's also shown up mostly as a bad guy in the Gotham TV show and the limited series Curse of the White Knight.
Besides Superman and Batman, DC also had replacements for the Flash and Green Lantern through most of the 90s. Wally West took over for Barry Allen after the Crisis on Infinite Earths event in the mid-80s and remained as the only Flash until Geoff Johns brought Barry back about 2009. After the Flashpoint event a couple of years later, Wally disappeared, much to the chagrin of many fans. He was brought back in the Rebirth event and was part of the Titans for a little while before in the limited series Heroes in Crisis he murdered a bunch of people, again to the chagrin of many fans. But just recently he was brought back to again be the main Flash in Infinite Frontier or whatever.
Meanwhile, after Coast City was destroyed by Doomsday, Hal Jordan went nuts and killed pretty much the entire Green Lantern Corps. A single ring survived to go to an artist named Kyle Rayner. For most of the 90s then Rayner was the main Green Lantern, until about 2004 when Geoff Johns brought Hal Jordan back. In the Blackest Night event, Kyle became the White Lantern, with power of all the various colors. He was a big part of the 12-issue Omega Men series but after that has pretty much just been a minor character in various Green Lantern and DC titles. He hasn't really shown up in any movies or TV shows to my knowledge.
What happened to Steel and Kyle Rayner is mostly what seems to happen. The replacement hero might have a spotlight series for a little while, but after it folds they just wind up as bit players. Maybe then it was for the best that Jane Foster's turn as Thor ended with her dying so no one at Marvel had to worry about what to do with her--though I'm sure she'll be back. Or maybe she already is; I haven't read a lot of Marvel comics lately.
Obviously there are more characters who could be added to this. It is kind of sad these characters get the spotlight for a little bit and then most get cast aside to be supporting characters again. It's like a "one-hit wonder" in music or someone who gets "15 minutes of fame" for going viral or whatever. Their star burns brightly but a short time and then afterwards it just glows dimly but can't ever get back to that point again.