If a player loses, do any emblems they create for other players disappear?
No, they do not disappear.

CR 800.4a reads (in part):


  When a player leaves the game, all objects (see rule 109) owned by that player leave the game.


And according to CR 113.2 (emphasis mine):


  An effect that creates an emblem is written “[Player] gets an emblem with [ability]...” The emblem is both owned and controlled by that player.


Therefore, the emblems do not disappear, because their owner(s) are still in the game.



The Gatherer rulings for Chandra state this interaction explicitly:


  Each player who gets Chandra’s emblem is the owner of that emblem. In multiplayer games, that emblem will remain in the game as long as its owner does, even if Chandra’s owner leaves the game.