[Elladan and Elrohir]

Responding to the very last thing you said, Earendilyon, it might've been neither.

Faramir cursed Gollum with "death, and may it find you quickly" if he proved false to his master.

Also, the Ring itself (or was it?) told Gollum that "if you touch me again, you yourself will be cast into the fires of Doom."

But, I of course believe it was the will of Eru, though it is notable that both of the above noted curses of Gollum came true.