Hehe, I like all the sentiments here (especially mourning particular parts of EU), but I suppose it could roll the other way, with a player character being such a huge prick (i.e. dark side), that the Empire just needs to deal with them (if a player is inclinded this way).
Oh, and I realised I didn't actually lay out my own example so here it is:
A member of the Jedi Order during TCW has a falling out with council (either personally, due to separatist sypathies, or over the ethos of fighing in a galactic war) and leaves the order. Fleeing to Corporate Sector space (probably playing to those sympathies) they hide out on the relatively lawless Ocsin colony of Saclas (by EotE times anyway) and are essentially stuck there once Order 66 travels out.
This character would probably be a mentor if I could ever scrape together a group to GM and the initial stages would probably involves PC's getting into some serious trouble with the Empire and the mentor (having forseen said particular event/s) has traveled to whatever planet they're hiding out on and saving their bacon, and things procceed from there and etc...