All damaging conditions cease doing damage if the person who cast the condition dies, even though the condition itself continues to tick on the target.
This is a problem for professions that have NPC allies that can inflict conditions, especially the Mesmer; because if you Shatter your Illusions or if they die to a sneeze all their conditions stop doing damage. For condition Mesmers, this can be devastating and makes Shattering almost completely non-viable.