Black Eye Guy
Taking over the World!
First and formost the Watcher's Council in pragmatic. By the end of 'Checkpoint' they're back working with the Slayer as she fights Glory/gaurds the hellmouth. There's no real need to worry about a rogue slayer in jail.
But if Buffy dies and no new Slayer is called then they have to deal with Faith, otherwise no more Slayers until Faith gets out of prison in possibly 25 yrs. (or busts out to help Angel in S4, but whatever.)
Yeah but that is a very different version of the Watchers Council to the one in the show. The Watchers Council never stuck me as caring that a slayer is out there projecting the world, they want that tool on their side.
If they were going to kill Faith just cuz Buffy died, they would have done it in season 4/5. They probably would have had Buffy killed too, if it meant they get control over the slayer again.