Do passives still remain active if a champ (who owns the passive) dies?
Example: Scyl has a passive that heals allies at the beginning of each turn. If Scyl dies, do the remaining champs still get that heal at the beginning of each turn?
The scyl passive heals when she gets a turn. She doesn't get any turns when she is dead, so no. But kram is correct, even if the passive healed for each of the other champs turns it would no longer apply after death.
I should clarify, actually - there are some champs whose passives explicitly state that they DO work even when the champ is dead. Lydia, for example, auto-revives when the enemy team tries to revive someone. But those are the exceptions to the rule.