Not a Companion, but she's had more than a few run-ins with the Silver Hand I'd imagine. Small villages, hamlets and towns throughout Skyrim have probably heard faint whispers of an especially potent werewolf of daunting ferocity that strongly exhibits a pattern of behavior that is wholly dissimilar to that displayed by the world's other werewolf denizens. 

Basically, she doesn't maul random people and can (to an extent) stave off the urge to slaughter anything living (and nonliving alike) that crosses her path. Granted, it's happened before (the first shift is almost always the hardest to contend with)--and still occasionally does happen--but these are now rare occurrences. This particular bit on her history will be rather grim to say the least. Suffice to say, the Silver Hand doesn't care how 'reformed' or 'in control' she is. She's still a monster and must be dealt with accordingly. 

Anyway, that sort of raw killing power stems from the character's status as a lesser champion of Hircine; the Huntsmen has taken a keen interest in the character due to her unique capacity to effectively utilize her werewolf form as a honed weapon rather than as an uncontrollable curse that haphazardly destroys whatever mortal or immortal entity that it comes into contact with. 

She's an efficient hunter and a natural-born murderer. Hircine, naturally, admires these aspects of his Hound very much. The Daedric Lord--along with the wolf that dwells within her mind---mutually whisper honey-laden words of comfort and temptation to the character in an effort to draw her closer to her patron. She's destined for the Wild Hunt and the Hunting Grounds. Hircine knows this, and the character fears it. Deeply. 

 More OT: Character contracted the disease in her backstory, she's not a Companion and she's probably seeking passage off of Skyrim in an effort to flee her past and those that are pursuing her. 

I am interested in that Lycanthropy quest line though. Any details?

EDIT: In case there were concerns of powerplaying on my part, I kind of envisioned this character being a wandering street beggar or pauper of some sort. It's a low profile profession, so I think it fits nicely. Decent hand-to-hand experience, but expert-level swordsmanship and sorcery is out of the question. Personal wealth is minimal and 'armor' probably consists of hide, rags and fur garments handcrafted from kills that she's scored in the wilderness. Useful group skills? Maybe pick-pocketing and picking locks. Remaining unseen works too I guess. Her technique is sloppy though and her lackluster skills probably didn't earn her a spot in the Thieves Guild I'd imagine.