Who does the Slayer lineage run through?

When Buffy dies the first time, Kendra and called. Although Buffy comes back to life, the Slayer line now goes through Kendra. So when Kendra is killed by Drusilla, Faith is called to take her place. When Buffy dies at the end of season 5, no new Slayer is called. A new Slayer will not be called until Faith dies. Of course, this all changes at the end of season 7.

The Slayer line passes through Faith. Sineya was created with the heart and soul of a demon, which passes to another potential on her death. There is not another new demon soul created because a Slayer died and was brought back. That Buffy still had her powers when she was brought back indicates that the demon's essence is only needed for the transformation, that it is one way, and that the Slayer's body simply hosts it until her death.

I would presume that if all the Slayers activited by the Scythe were wiped out, no new potentials would be called until Faith died.

I have been binge-watching Buffy for the last month-and-a-half rewatching it from what I can gather when Buffy died Kendra was activated when Kendra died Faith was activated So the activation after Buffy had already occurred so even though Buffy was brought back for the next Slayer in line it would have to be Faith to die and it never said that Faith didnt died temporarily at the hospital when Buffy put her in the coma but if she did and another potential was activated the council may not have known or told anybody but if she didn't die it would still be her and just Buffy.

Buffy's (second) death didn't result in the calling of a new Slayer as hers was no longer the "active line".

New Vampire Slayer Wanted? by Charlie Mason

Where's the Watchers Council when you need it? Historically, every time that one Slayer is killed on Buffy the Vampire Slayer, another is magically drafted for active duty. Heck, back in the first season, Buffy (Sarah Michelle Gellar) only stopped breathing for a matter of seconds before a successor, Kendra (Bianca Lawson), was dispatched to Sunnydale. So, after Buffy spent the entire summer pushing up daisies, how come no new Slayer has been called to arms? Has the show forgotten its own mythology?

"We actually have an answer for that," executive producer Marti Noxon tells TV Guide Online. "It's a technicality. The reason [Buffy's demise didn't activate another vampire hunter] is that when she died the first time, a Slayer was called, so she's already had her replacement Slayer.

"It doesn't happen twice," she continues. "You only get one, and Buffy already did."

The fact that Kendra quickly kicked the bucket, and her next-in-line, Faith (Eliza Dushku), is behind bars makes no difference to the powers that be. "Since Faith is still alive," Noxon notes, "the line remains intact."
So, in other words, viewers shouldn't look for another stake-toting teenager to turn up in Sunnydale anytime soon "” at least not unless Dushku's burgeoning film career takes a dive. "It would take Faith dying for another Slayer to be called," Noxon says, "and since we can't get [Dushku] on the show, the odds of that happening aren't big."

_{^{Buffyboards.com quoting TV Guide}}

So, in the absence of Faith dying, no additional slayers will be called.