In recent years the internet has been ablaze with rumors based on excerpts from the original games. The game suggests that due to your rival battle on the S.S. Anne, your rival’s Raticate dies. Now, as a child it’s often overlooked, after all, have you ever seen a Pokémon die? No, because it’s a kid’s series. The Pokémon Graveyard in Lavender Town suggests that Pokémon can die, but it is never explicitly stated how they die. Never the less, you, the player are responsible for the death of Blue’s Raticate.
The theory suggests that the S.S. Anne battle left Blue’s Raticate with series injuries. Because of the commotion onboard the S.S. Anne and the constant harassment from over eager trainers with the desire to battle, Blue was unable to reach a Pokémon Center in time to heal his Raticate, thus leaving it to die from its wounds. The theory is backed up by the rival’s comments when you see him in Lavender Town.
Hey, RED! What brings you here? Your POKEMON don't look dead! - Blue, Pokémon Tower
In every fight after that point Blue is missing his Raticate and while it is possible it died there is also counter theory to suggest that it is still alive in his PC Box. Blue boasts to Red before one battle that he has caught over 40 different Pokémon, yet he only keeps four of them in his party. Why? It is most likely due to Blue’s drive to win. Blue probably only trains Pokémon he finds will be worthwhile to him in the long run. Once his Raticate outlived its usefulness he probably traded it in for another Pokémon. Why then was he at Lavender Town asking Red about the deaths of Pokémon? Maybe it was a sarcastic comment based around the logic that he’d beat Red so badly that Red’s Pokémon would die.
Either theory is plausible however; I personally prefer the Raticate dying scenario because I feel it provides a new depth to the game, even if it seems inconsistent with Blue’s personality and training style.