It is currently unknown what caused Droz and Davis to leave the 6-4 and form The Last Resort.
The Last Resort, while appearing in Titanfall 2's multiplayer, are not selectable outside of Frontier Defense. They additionally do not have their own ranking system like those of the other seven factions, meaning the player will have Davis and Droz as announcers but will level up their selected faction independently.
Occasionally, Davis will celebrate victory by saying "That's how the 6-4 does it!", to which Droz will reply "We aren't the 6-4 anymore, Davis". Davis will either reply by correcting himself and saying "That's how the Last Resort does it!", or (less frequently) "Six-Four-evermore, Droz, Six-Four-evermore!" This implies Davis still respects the 6-4 by reusing their motto, and that perhaps the separation was more because of Droz's encouragement. At the very least, it means they left on good terms.