Is there an event that is triggered when a player dies?

Yes, there's an event of Humanoids for when they die.

--LocalScript in StarterPlayer.StarterPlayerScripts

player = game.Players.LocalPlayer
repeat wait() until player.Character
character = player.Character
humanoid = character:WaitForChild("Humanoid")

humanoid.Died:connect(function() --Using the "Died" event of Humanoids
    print("ded")
end)

Unfortunately you won't be able to know who killed him, only when he died. So no, you can't use this to directly award points to the killer. You'll have to figure something out.