From what I understand, emblems are continuous effects that apply throughout the game, even after the emblem's controller dies. And if the emblem involves a trigger, such as on Sorin, Solemn Visitor, the player who ultimated Sorin is responsible for remembering the trigger. So if that player dies in a multiplayer game, and the emblem still exists, can the other players simply choose to ignore the trigger since they aren't its controller?
When a player leaves the game, emblems they own leave the game as well. You own an emblem if you “got” that emblem when the effect that created it resolves. Three planeswalkers can create emblems for opponents, and those opponents own those emblems and they will persist even after the player who created them leaves the game. Players are responsible for the triggers of emblems they own.