We ARE talking about FF2 here (SNES version, at least)

Anyways, I have a theory on the survival of Cid and Yang. Never fear, it involves Cid's beard.

It's all because everyone in the FFIV world worships Chuck Norris. The only reason they never speak his name is because Chuck forbids it. Cid and Yang were the high priests of Baron and Fabul respectively. They show their position by emulating Chuck in some way; Yang's kick attack was in honour of the roundhouse kick, and Cid tried to look like Norris in beard and physique. Chuck Norris was proud of his two most faithful disciples, and so performed miracles to show to the world his power and his mercy; he roundhouse-kicked Yang into the Slyph cave moments before the room exploded (Yang's screams of pain were not due to his flesh burning, but the far more painful experience of meeting with the foot. Cid, on the other hand, Chuck switched with a figurine of himself, which he mentioned in passing to one of his many girlfriends, Marle, and inspired the switcharoo event in Chrono Trigger. He then took Cid to the Dwarven Castle. Both of them were sworn to secrecy, since Chuck Norris told them he'd be back, to destroy the world, if they ever told anyone. EVER.