The Curse of Fire is a curse started by The False Prophet making it that all fire types trying to make it to the Hall of Fame are released.
Red's Eevee was meant to be a Vaporeon. She refused and became a Flareon. This "betrayal" to some resulted in a curse of fire types, where each one would fall. Abby was the first to die, and then the prophet herself.
Zexy, a Torchic, fell due to the Curse of Fire. The voices warned A of what would happen if she chose Torchic, but she didn't listen.
Lazor Ape, a Chimchar, fell. Solaireon, the Sun Prophet and another Flareon, set out to break the curse started by one of his kind by reaching the fall of fame, which he did, breaking the curse.