I think one of the most chilling lines in Tolkien is when Gandalf’s talking about Gollum and he says the Woodmen had started telling stories about this new terror that “slipped through windows to find cradles.”
Gollum ate babies.
Alternate theory: Gollum is the tooth fairy. When he’s diving for fish he keeps finding coins that people threw in the pond for good luck. He has no use for the coins (since it’s not like he’s just going to walk into a store), so he’s taken to exchanging them for teeth.