How did Asuna and Kirito survive? In the last episode of Aincrad arc of Sword Art Online, how did Asuna survive even though her avatar disintegrated after being attacked by Kayaba? Also Kirito was stabbed by Kayaba as well. How did he survive?

Was it in the novel on how they really survived?
Asuna

Theory 1: Kayaba kept his words to prevent Asuna from comitting suicide

Before the fight, Kirito had requested Kayaba to prevent from Asuna taking her own life if he was to die, as Asuna threatened to commit suicide if that happened. Quite possibly, Kayaba had set thing up to ensure that if Asuna went to kill herself, she wouldn't actually die, confident that he would win (as he was supposed to be the last boss on the 100th floor).

Otherwise, in my answer to the question Mysticial linked to, I explain there is a time delay before the NervGear kills Kirito in the real world. Seeing as Asuna had in a way killed herself, Kayaba at that point might have prevented Asuna from dying in the real world and put her in the holding area where she met with Kirito later. After all, Kayaba was show to have a level of honor and fairness and probably wanted to hold up his end of the deal. Remember that he paralyzed everyone so no one would get in the duel between him and Kirito, yet he was surprised to see that Asuna was still able to move.

Theory 2: Sugou had been keeping Asuna alive

Another possibility is Sugou Nobuyuki. Asuna being in the holding area may have been a stroke of luck, and Kayaba didn't notice that after SAO was cleared, Sugou prevented 300 players from waking up for his experiments. However, this runs off the theory that Asuna was not just one of the 300, and she was targeted to be isolated and trapped separately. 

This is slightly backed up by 2 points:


Sugou did say he was keeping Asuna alive, rather than her father who owned the company, and were more likely to use it to look after his daughter
The wiki about RECT Progress's background says


  RECT Progress Inc. had set the 1st main goal of ALfheim Online to reach the top of the World Tree, but was later found to be impossible to complete. It was revealed that the World Tree's actual purpose was to hold the remaining 300 prisoners from SAO as test subjects in inhumane experiments.


This would indicate that since the release of ALO, Sugou was waiting for SAO to be cleared.


Kirito

As for how Kirito survived, please refer to my answer here. (Originally, this question only addressed Asuna, and I have only noticed that it's been edited to address Kirito as well).