Luck and timing. The players apparently asked for less chaos and Staios agreed. They already fired Dorion, and had the Pinto debacle. Those are multiple chaotic situations. Add in the timing aspect of the ownership changeover not taking place until the end of the off season, and there wasn't time to do a proper coaching search if they wanted to do one.
I can see the logic in keeping DJ. A new coach is unlikely to turn the season around. It's statistically unlikely for a team to make the playoffs down this far in November. Get the goodwill from the core players by not firing DJ in season, and then in the off season when the management group is in place, make the right choice.
If they bring in a coach now, maybe it turns things around, but it probably won't. So then they're in a scenario where the players feel the new management didn't have their backs, and they went against their promise of less chaos for nothing.
They are in a solid situation now where they will have the manufactured consent of the players and fans to make whatever radical changes they want to make in the off season because they can say we gave DJ and we gave this core a chance. Changing coaches and possibly sparking a slightly better finish that still probably won't be good enough for the playoffs would go against that.