The following contains spoilers for DC vs. Vampires: All Out War #2, on sale now from DC Comics.
In the midst of a vampire apocalypse, a bright future doesn't seem to exist. In the DC Universe, the future is an important part of the heroic landscape. The actions of Earth's heroes -- Superman, in particular, led to the creation of the Legion of Superheroes in the 31st century. However, with Superman having been turned into a bloodthirsty vampire, along with many other inspirational heroes, the Legion's once-promising morale of striving for a better tomorrow is far out of reach.
With that in mind, one of the heroes in DC vs. Vampires: All Out War #2 (by Alex Paknadel, Matthew Rosenberg, Pasquale Qualano, Nicola Righi and Troy Peteri) shouldn't exist -- and he knows it. It might have surprised some to see Booster Gold as part of the human resistance in the previous issue, and he got a bit more of the spotlight this time around. In the middle of the action, he even pointed out that he shouldn't even exist, as his timeline is no more.
Nevertheless, Booster Gold is there, and it doesn't look like he's disappearing anytime soon. Perhaps one of the most common examples of messing with time and time throwing it right back at you is the movie Back to the Future. In the classic film, Marty McFly accidentally prevents his parents from getting together and in doing so, starts to fade away. He eventually sets things right, but it's a firm example of how poking around in the past could eliminate a time traveler's existence. And that may be what Booster expected to happen here.
However, something similar happened in the world of Injustice, with the Reverse Flash (Eobard Thawne). On that Earth, Barry who was siding with Superman erased Thawne's timeline, changing the future. Therefore, the Reverse Flash should never have existed, but somehow he was still around, plaguing Barry for destroying his home. Eobard even similarly remarked on his timeline not existing anymore.
What happened to Booster and Eobard could be examples of the parallel timeline theory. Fans of comics may recognize it as the basis for Avengers: Endgame's depiction of time travel. In this version of the popular sci-fi trope, changing the past doesn't destroy the original timeline of the time traveler. Rather, it creates a new one that runs parallel to it, whilst the original cannot be accessed anymore, it still exists somewhere.
Often, larger worlds like DC and Marvel end up messing with several different time travel theories and never creating any concrete rules. That's what happens when one creates a world with hundreds of different stories from hundreds of different storytellers across literal decades. Clearly, even a smaller scale project like the Back to the Future trilogy mixes up its rules. So, it’s no surprise.
That's where all the nerds come in. Doctor Who is a prime example of time travel-centric media tackling every single version of time travel possible. A lot of the time it actually works, and contradictory paradoxes and parallel timelines can exist in lots of different points in space and time -- with a little creative rule-bending and explanation that is. Even still, it's mostly up to fans to decide how all of these discrepancies can fit together, often with large sprawling theories and the occasional equation. Everyone else, however, usually just ignores the plot holes as best they can and enjoy the show.
For the readers of DC vs Vampires, the simple answer is that Booster still exists because this is a parallel timeline now. His future still exists, but it's lost thanks to the actions of the vampires. He won't fade away like Marty, but he can never go home. Another explanation is that time is always in flux and any number of possible futures can exist, and as long as those time travelers stay in the present, which is not in flux, they'll be safe from the constantly changing timeline they traversed to get there. That's more on the complicated side, though. For those seeking simply to enjoy this universe and not sweat the details, just sit back and enjoy the ride as the series unfolds.