When you encounter your rival in Pokemon Tower, he will ask you why you're in the tower to begin with because you don't have any dead Pokemon to mourn over. This implies that he has lost a Pokemon and has come to pay homage to it or lay it to rest. Furthermore, his Raticate from the previous battle on the S.S. Anne is replaced by an Exeggcute, Growlithe, or Gyrados, depending on the starter Pokemon you chose. This seems to imply that his Raticate somehow died between the battles against him on the S.S. Anne and in Pokemon Tower; common fan speculation states that the Raticate died from wounds received from the battle on the S.S. Anne.
Contributed by game4brains
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