The basic background for this character would be the same no matter the race or gender. (Let's say he or she could be adopted to have a consistent first and last name; the first name could also be gender-neutral.) The voices could be the same for all human and elf versions; orcs, khajiit, and argonians would obviously need different voices. The character would be a follower as well as a marriage option.
The character could be included in a future quest. It could be a small but enjoyable one, perhaps a very adventure-themed journey or an already existing/in-the-works DLC. (Yes, god knows what it would take to do it, but I'm not a programmer, so...I'll just let my big mouth/typing fingers continue.)
A Scenario (no, I haven't overthought this, why?)
I like the idea of your player character joining up with this stranger on an adventure. Perhaps her birth family was murdered and she mistakes you for someone who did the deed. Then, after besting this individual in a fight, you can help her on her quest. But do you bring the murders to justice or allow your new traveling companion to take revenge to its fullest? I imagine this would have the feel of the Oblivion DB quest "Whodunit?". The stranger's birth family was killed when she was a child and years later she is tracking down those who did it. Some of them have moved on, become members of society, others have become worse...
I'm sure there are better ideas than mine; just throwing it out there as an easy conceit. I'd lke to see any scenarios anyone else would have.
Anyway, this was just a thought I had for something that I've had on my personal wishlist since followers were introduced in Skyrim.
Edited: spelling