Does Jun survive the Covenant war?

Yes, Jun A56, the SPARTAN-III character from the Halo series, survives the events of the Covenant War. He is one of the few surviving members of his team, and after the war, he takes on a new role as a trainer for the next generation of Spartans. His fate is explored further in the Halo: The Fall of Reach novel and subsequent media, where he remains an important figure in the ongoing fight against threats to humanity.