This is pretty much the definitive answer. 😉
When Eliza went to audition for Buffy she was only supposed to be in it for 5 or so episodes.
The plan was for Faith to kill somebody by accident and then take her own life in guilt/remorse. The plotline would reveal that being the slayer, with all that darkness inside you, could cost you in a different way if you lost control.
Faith would be the out-of-control slayer who lost her grip and fell into darkness, but in a very different way.
But Eliza impressed a lot of the crew (and Joss of course) as Faith so much and he saw real potential with the character and just kept on adding scenes with Faith in. (It's why she's absent from some episodes, like 'Gingerbread' and 'Helpless' for no real reason)
It mirrors JM's role as Spike in many ways, since he was meant to die at the end of 'WMY part 2' but thankfully the writers saw his potential and went a different way.
(Fun fact: Lover's Walk was meant to mark the return of Spike AND Dru to Sunnydale, as a happy vampire couple causing havoc, but they couldn't get Juliet Landreu so they instead had to go with a heartbroken Spike- which in turn led to Joss seeing more depth to his character- so he returned in S4...and the rest is history)
I remember Eliza saying in an interview that half the Faith lines in 'Choices' and 'Graduation Day' were written on the fly- especially the ones between her and The Mayor.
Joss would run off and amend a script to give her more lines about Faith's childhood, or a turn of phrase that Eliza herself used. There's a lot of Eliza in Faith's character, which is why I think Eliza has a lot to draw upon in the role. 🙂
Then Joss decided NOT to kill Faith off at the end of the Season and instead to put her in a coma. All so he could bring her back for a redemption arc that would end on the show 'Angel'.
The fact that it all seems (mostly) so seemless is just skilled writing.
Oh, and Faith's from BOSTON, not Cleaveland. Nothing wrong with Boston. 🙂