Which "end of round" effect resolves first: dealing in a dead player, or game end due to low honor?
The game ends, the player with zero honor doesn't get a new ninja until just before a new round starts, and only if the round hasn't ended. In the rule book under Phase 8: Check Honor, besides the checks to see if the game has ended because a single player has 5 more honor than every other player, or the franchise honor is so high or low that the manager's position becomes open, it says this: 


  If no one has won, a new round can start. Before the round starts, though, any ninjas whose Honor has gone to zero or less must make amends ...