Well, one of the theories is that Ultimecia is indeed Rinoa in the future, assuming an alternate reality took place where Squall and the SeeD weren't there to defeat her. Therefore, the Griever that Ultimecia summons is the Griever in Squall's necklace, which he ultimately gave to Rinoa, who then took it to the future with her as she became Ultimecia and used it the battle agains Squall just as pretext or whatever.
To answer your question, I believe Griever dies after the battle, Odin was killed by Seifer, the same way Squall and co kill Griever and almost killed Bahamut and all the other GFs you're able to acquire through battle.The only difference is those GFs chose to offer their services to you instead of dying and Griever was being controlled by Ultimecia, ultimately not being able to offer his services to you and dying instead.