Here are some possibilities I've considered:
1.) The most unlikely case, take the scenerio at face value. Brienne somehow escaped her hanging, Sansa escapes the Vale and the Hound is still out there alive. Jaime realizes his love for her and they get it on? Very unlikely but you never know with Georgie.
2.) Brienne is leading Jaime into a trap to save the lives of Ser Hyle and Podrick. Perhaps the word she yelled out was "Jaime!" or "Kingslayer!" Although Brienne's fondness of Jaime and whole honour and oathkeeper thing makes this seem unlikely, being on the edge of death can change a person in such a way. Maybe Cersei will lose the trial by combat, and her and Jaime will be excecuted simultaneously. "We came in this world together, we will leave it together..."
EDIT: I'm aware GRRM confirmed the word to be "Sword!" but the same idea applies.
3.) Brienne was hung, but the word she yelled before she died made Catelyn realize she was wrong to hang her. She passes on the "Kiss of life" to Brienne. Jaime described Brienne as looking 10 years older, but that could also just be a result of her feverish episode after her encounter with Biter. This however would explain Brienne's reason to lead Jaime into a trap. Both Beric and Catelyn were described to be "different people" in their ressurected forms.
Or maybe it is a mix of one of these theories, or something completely different altogether! What do you guys think?
Edited by Lord Davos Seaworth, 29 January 2013 - 02:18 PM.