See, the Chris Claremont and Frank Miller's 4-Issue Wolverine series was a great hit. Marvel naturally wanted more - so they pushed for Wolverine to have his own on-going series. Chris Claremont wrote the series, but felt that Wolverine didn't need his own book. He was, of course, one of the X-Men -- and already got his share of the limelight in that title. So Claremont took the series in a direction that he thought would only be interesting to him. He featured Wolverine having adventures in the fictional city of Madripoor, an island in Southeast Asia. Giving Wolverine a very noir setting, with criminals everywhere, the feral mutant fit right in.
But what I find really strange is the timing of this series - as at the time the X-Men where believed to be dead. They where all hiding out in Australia - and Wolverine, I think, was hitching rides to Madripoor to hang out on his own. This left Claremont with a problem - how can Wolverine be strutting around, having adventures, is he's suppose to be lying low. To fix this, Claremont gave Wolverine the new identity of "Patch". Wolverine just put an eye patch over his left eye, utterly disguising him from friends and foes! That's bull when you think about, because Wolverine, while not in his regular costume, is always very identifiable by his hair, attitude, voice, everything. No one was fooled by this, and to try and believe his friends and enemies where deceived is kind of a joke, or at least made his friends immensely stupid. Jessica Drew, aka Spider-Woman, even appeared in the series - and Wolverine had been crashing at her Sanfrancisco home for the past year, along with all the other X-Men. How the heck could she not recognize Wolverine? When Peter David took over writing for the book, he even had a moment, when Wolverine finally put on his regular brown and gold outfit, that no one was actually fooled by "Patch".
Heck, Wolverine even came back from missions without the eye patch! Issue #5 has Wolverine hitching a plane ride with a buddy. When he comes back, he's not even wearing the eye patch anymore - and nothing about it is said. Wolverine was trying really hard, too - only popping his claws in secret or when fighting enemies. He thought he was being so cleaver.
Basically, to make sense in my mind - people just played along with Wolverine's game, and in fact no one really cared if the X-Men where alive or not. I mean, really, unless you wanted to get rich by ratting them out to their enemies, you just wouldn't give much care. Only Cyclops, then on X-Factor, might have been interested that his ex-wife was still alive in Australia. Everyone else, especially in a dump like Madripoor, could care less.
Despite all this, Chris Claremont's issues where very fun, if not different from regular X-Men fare. We got a great new environment that the Marvel Universe has been traveling back to ever since. With all the awkward effort put into tanking this series, Chris Claremont left the series after only 8 issues, and Wolverine went on for 189 issues! And some of those stories, after Claremont left, really sucked. A true testament to the popularity of Wolverine, even if you're trying you're hardest to make him unpopular.