Brian dies just as Mick takes Marianne to Australia to film the Ned Kelly movie.  Marianne is already fucked up on junk and Mick is not far from dumping her.  She ODs on pills and ends up in the hospital.  When she wakes up, Mick is there and says something like "I thought I lost you" and she responded "Wild horses couldn't drag me away." 

Meanwhile Keith is doing his country thing with Gram Parsons and has this new melody.  They get together and Mick drops in the new lyrics he's written, and the Stones record it on a break from the US tour in Muscle Shoals Alabama.  I think a version by Parsons' Flying Burrito Brothers actually pre-dated Sticky Fingers.