In the 2nd rules is written : When an Untimely Death is played on
a Character, set aside that Character
card along with all the cards that have
been played on it.
So understood this, the dead charakter is not more in the game
but out of game with all cards puted on them.
I'm pretty sure the story icons of dead characters are explicitly included as still part of the game in the rules. At least in Cthulhu Gloom (which is the version of the game that first included a major mechanic based on how many of each icon you controlled) if not in the regular version.
Also, there are many different cards which explicitly can be played on an already dead character, so stating that they're out of the game is simply not true. They may be put aside to make clear that they're dead, but they are very much still a part of the game.