Saphira

Oromis paused, his face grave. “Do you know why losing your dragon, or vice versa, usually kills the survivor?”

“I can imagine,” said Eragon. He quailed at the thought.

“The pain is shock enough—although it isn’t always a factor—but what really causes the damage is feeling part of your mind, part of your identity, die. When it happened to Brom, I fear that he went mad for a time. After I was captured and escaped, I brought him to Ellesméra for safety, but he refused to stay, instead marching with our army to the plains of Ilirea, where King Evandar was slain.

On the crags of tel’naeir pg 423 Eldest