Suzy's Vulpix is a Pokémon owned by Suzy, who was gien to Brock for some time.
Through seeing the care that Brock went into in looking after Pokémon, Suzy decided to let Brock look after it. Brock was often seen grooming it and sometimes used it in battle, mostly however in training with Ash. Vulpix, while a little bit spoiled, did enjoy playing about with the other Pokémon. Eventually Brock met up with Suzy again and decided that Suzy should keep Vulpix.