User blog comment:KillRoy231/Is the game canon?/@comment-89549-20180227183531/@comment-1031724-20180227215548

All right, I did some research (ironically on the 12th anniversary of the game), so here's my interpretation:

David Palmer goes back into office during the game, so it must have been after it - and therefore after Max's death - that he arrests "the man behind the attempt on his life" and exposes his organization.

Therefore, it follows that Trepkos (who must have been aware that Max was behind the assassination attempt by then and would likely have helped him try to get away with it) assumes leadership of Max's organization following his death, so that when Palmer finds and exposes his organization, Trepkos is seen as the man behind the attempt on his life (or at least the surviving one of the two), which, according to Season 6, carries the death penalty, so Trepkos was likely executed before Day 3.