He goes to ONI Castle Base which is the mountain with the hole down the center of it in the final cutscene. ONI Castle Base was attacked by the Covenant during the fall of reach because of a crystal that the Forunners used to modify slipspace. The hole is there because of the fact that the crystal was deep in the Titanium mines below the mountain. It is most likely that Jun died or was evacuated because when spartan blue team fell back there the only person in the base was Dr. Halsey. If you want a more detailed account purchase the book "First Strike".he dies from remaining covanet forceshe flies of in to the sunset.