my theory is tat since in the book (i havnt read them but i hav heard bout them) tat master chief and others from halo come bak and rescue dr halsey and others from reach. either master chief saves them and jun and he goes with dr halsey and other spartans to shield world or he dies protecting her

Bungie confirmed Jun is alive by the End of Halo: Reach

Whether he survived the Human-Covenant War is up for Debate
but I do believe he quit after Escorting Halsey.