Even though it's not one of his mutant powers, Wolverine seems to have a supernatural ability to be in two places at once. In any given month, Logan may find himself on seemingly simultaneous missions with the X-Men, X-Force, the Avengers and all by himself. Taken with any other guest-appearances of Marvel team-ups he might be involved in, it almost seems like there's more than one Wolverine running around the Marvel Universe.
In 2013, Brian Michael Bendis, Bryan Hitch, Brandon Peterson and Carlos Pacheco made that idea a reality with the Age of Ultron crossover. Although that story bears little resemblance to the Marvel Cinematic Universe movie that shares its name, this titanic, time-twisting tale engulfed the entire Marvel Universe. As Marvel's heroes turned to increasingly desperate measures against the Avengers villain, the Marvel Universe ended up having two versions of Wolverine, and it's not entirely clear what happened to one of them after the crossover came to an end.
Age of Ultron begins with the worst day in the history of the Marvel Universe. After a lengthy period out of view, the Avengers' robotic foe Ultron returned with a massive android army that conquered the world in a few minutes, killing billions of civilians and dozens of superheroes.
In Bendis and Hitch's Age of Ultron #5, Marvel's surviving heroes regroup at one of Nick Fury's hidden bunkers, where he's hidden a stash of superhero and supervillain weapons. After Captain America and a few other heroes use a time machine there to travel to the future to stop the base of Ultron's attack, Wolverine uses it to go into the past and kill Hank Pym, the original Ant-Man, before he can ever create Ultron.
Accompanied by the Invisible Woman, Wolverine journeys to the past and successfully kills Pym early in his superhero career, roughly around the events of 1967's Avengers #42, by Roy Thomas and John Buscema.
However, Pym's death execution causes more problems than it creates. Without Pym on the Avengers, the Marvel Universe was devastated by events the Kree-Skrull War and a war between Latveria and Asgard that left much of the world in ruins. Horrified by a world that was even worse than the Age of Ultron, Logan was sent back in time again to stop his past self from killing Hank Pym.
In Bendis, Peterson and Pacheco's Age of Ultron #9, these two Logans met in front of a very confused Hank Pym. Everyone present ultimately agrees that the best way to proceed -- without breaking history -- is to have Pym implant a hidden killswitch deep within Ultron's programming.
Having effectively fixed the timeline, the Age of Ultron Wolverine who initially went back in time has the other Logan kill him to avoid creating a time paradox. After that, the surviving Age of Ultron Logan and the Invisible Woman travel back to the main Marvel Universe, which largely exists as it always did.
After briefly looking at the world he saved, this Wolverine is seemingly caught in a timequake that shakes every corner of the Marvel Multiverse. Even though his time-hopping actions were a big part of what caused the timequake, Age of Ultron's Wolverine did not appear in any of the stories that followed up on the various ideas introduced in the crossover.
While this Wolverine could have been somehow erased by one of these timequakes, this Wolverine's ultimate fate is left decidedly unclear. From Heroes Reborn's Bucky to the survivors of the Age of Apocalypse, plenty of other Marvel characters from other timelines have lived on in the Marvel Universe after the apparent destruction of their home timelines, and there's no reason to think the same couldn't hold true for Logan.
Even though this Logan hasn't appeared since Age of Ultron, Marvel embraced the idea of a second Wolverine in the years following the crossover. After main Logan's death in Charles Soule and Steve McNiven's Death of Wolverine in 2014, alternate reality Wolverines like Old Man Logan and a Phoenix-wielding Wolverine took his place in the X-Men and the larger Marvel Universe until his return last year.
The Marvel Universe has been through a few reality-reshaping events since Age of Ultron's Wolverine first landed there, and he could've easily been erased off-panel. However, this Wolverine has slipped through the cracks in time before, and he may very well have done so again. Whether he was erased from the timeline or is merely keeping to the shadows, Age of Ultron's Logan proved that he's still the best there is at what he does, even if the world forgot that he existed.