What would have happened in The Lord of the Rings if Bilbo Baggins had killed Gollum when he had a chance during the events ...

Why did the Nazgûl never chase after Gollum or Bilbo when they were in possession ... That someone just happened to be Frodo Baggins of The Shire.

Gollum. Here, alone with Gollum, on the shores of an underground lake, the unassuming Bilbo Baggins not only discovers depths of guile and courage that surprise even him, he also gains possession ...