Can a player lose their last army?
From the core rules:


  You may never enter a region occupied by an opposing player’s last meeple
  (i.e., the only meeple they have in play), nor may you use your last meeple to
  enter a region occupied by an opponent.


From the solo rules:


  If [the meeple] cannot move in the selected direction, continue clockwise until you find a region it can move into.


and


  The dummy player may always collect resources if they are unable to fulfill the action, even if they are the active player.


So suicidally throwing away your last army is illegal for both real players and the dummy, and the dummy will choose a different place to move instead (or collect resources if there are no legal moves).