Well, it's doable. For example, the character might cross a technomancer (for example by selling his hide to the corps), who'd be after him in the matrix. That enemy wouldn't want to kill him outright, just make his life a living hell. And his appearance wouldnt have to cause problems to other characters - he might be over it, and not tell them that their 'friend' is a double-crossing bastard. He'd cause a lot of problem anyways - virused warez and equipment, social problems (like putting his number on a troll porn lovers node, for example), and being cut of from the Matrix (or risking serious harm - the player doesn't have to know the rules of engagement), losing contacts (who might have been tipped off, or just harrassed/antagonized), the Enemy alerting the corporate security on his accurate position and objectives during a run, and so on... That could be quite easily recreated with a Magician, just through the use of ritual spells and spirits - just like the 'Accident' entry in Dunkelzahn's will.
Don't get me wrong, the Enemy would just want to utterly humilate the character, before he deals the final blow... And the character doesn't even have to be guilty - he could be the next best thing (a relative, friend, or lover) of the intended, but unavailable target. Or the Enemy could just be wrong about him - mistaken, misguided, or manipulated (by a Magician for example - the 'True' Enemy; this way you have two of them, both on manageable level).
Now, imagine how that would work with one of two other negative qualities - Escaped Clone, and Evil Twin. I had an 'evil GM grin' when i've thought of it...
The poential for great opportunities, both in terms or plot, character development, and roleplaying is indeed there. But as some of you noted - the whole party has to agree on it. And the enemy would have to be a recurring BBG, and an important part of the storyline.