The Legend of Korra

Buh, yeah I was having a hard time finding it. The copyright watermarks in the sound result in all of the youtube videos being horribly...awful.

 Spoiler

Linked to direct times;
http://youtu.be/CnjkA75GSwE?t=4m22s Aang "dies" and the Avatar State/cycle is lost. (Although I guess it actually doesn't show the past avatars disappearing, confirmation: friend is crazy.)

http://youtu.be/rkv-c3np4fM?t=4m18s By, what appears to be being jabbed in the scar from when he "died," everything comes rushing back.

Azula and the rest of the Fire Nation had every right to believe the cycle had been broken if that fact was known, regardless of whether or not Sozin's Comet was coming. Zuko, however, knew about Katara's water because she tried to heal his scar with it, so he knew that Aang probably survived. Remember how pissed off Ozai was when Zuko confronted him during the invasion and told him the Avatar was actually still alive? When they were searching for the Avatar and offering a hefty reward for him, they did not want him dead because he would be reborn and they'd have to start the search all over.