"Kool-Aid Claire" is an orchestral piece from the Season 6 soundtrack.
Sawyer convinces Kate to head for the Elizabeth, even if it means abandoning Claire. In the jungle, meanwhile, Claire and Jack talk. Claire says she stayed with Locke because he was the only one who didn't abandon her.
During their conversation, Sawyer talks of Claire "drinking Locke's Kool-Aid", a reference to the Jonestown massacre.