When The Lord of the Rings begins, Frodo Baggins lives with his uncle, who took him in after his parents died in a boating accident. Although their deaths were ruled an accident, local hobbits suspected foul play. With no confirmed witnesses, the truth may never be known, but a compelling fan theory suggests Gollum may be involved.
Frodo’s parents, Drogo and Primula Baggins, both died when he was still young, so Bilbo took it upon himself to raise his orphaned nephew. Frodo never has any reason to question why or how his parents died in the novel, but a fan theory suggests their deaths were not as straightforward as they seemed. The official story was they both drowned in a boating accident on the Brandywine River. However, the local hobbits, known for being talkative and forthcoming, gossiped about the details and shared second-hand tales regarding the deaths.
In The Fellowship of the Ring, Drogo is described as “partial to his vittles,” so when the topic of his death came up, a hobbit called Old Noakes noted that he'd heard Drogo’s weight sunk the boat. Another hobbit, Sandyman, went so far as to say, “I heard she pushed him in, and he pulled her in after him.” While this may be gossip, it shows some hobbits were suspicious of Primula and Drogo's passing. Of course, other hobbits, including the Old Gaffer, believed it was truly an accident. “Boats are quite tricky,” and hobbits are not comfortable around water, he said. Nevertheless, this does not rule out the possibility of foul play, and there were no witnesses to prove otherwise.
Before he found the One Ring, Gollum was a Stoor Hobbit named Sméagol. Stoor Hobbits were river people and fishermen. This means that, unlike most hobbits, Gollum was comfortable with water -- and murder. He killed his brother Déagol after they found the One Ring, and he was ready to kill Bilbo after Bilbo took his “precious” in The Hobbit's "Riddles in the Dark." In fact, even after Bilbo left the caves beneath the Misty Mountains, Gollum hunted the nasty “Bagginses.” However, he did not have much to go on -- only a name, “Baggins,” and a place, “Shire.”
However, sometime between the events of The Hobbit and The Fellowship of the Ring, Gollum (mostly) gave up his hunt. Frodo actually asks Gandalf the Grey why in The Fellowship of the Ring. The wizard responds that Gollum “set out and came back westward, as far as the Great River. But then he turned aside.” In The Lord of the Rings, the “Great River” would typically be a reference to the Anduin. However, at this point, Frodo had never seen, nor had any reason to know of, that river. The largest river Frodo knew was the Brandywine -- the very place where his parents died.
Considering Gollum is still looking for the Ring in the trilogy, he proves not easily deterred. So, the most logical explanation for discontinuing his hunt is that he believed he partially accomplished his task; he drowned the hobbit called Baggins. He got revenge but did not find the Ring, which is why he is trailing the Fellowship at the start of The Lord of the Rings trilogy. Gandalf tells Frodo, “[Gollum] was not daunted by the distance, I am sure. No, something else drew him away." Perhaps Gandalf knew the truth about Frodo’s parents and was keeping it from him. Regardless, without exact confirmation of Gollum's whereabouts, the theory remains plausible.