Stufful is part of
Bewear's family according to the English dub while the Japanese version in
SM96 states that they are parent and child (親子). One day,
Wicke was out on patrol all by herself when she heard a squeaking in the forest. She found this very frightened little Stufful's legs were pinned under a fallen tree and it couldn't get out from beneath it. She dug it out and took it back to the Aether Paradise where it had been serving as its caretaker and making a special point to look after it.
Team Rocket showed up at the Aether Paradise and began to plot how to steal all the Pokémon there. Stufful smelt a scent on
Jessie and latched onto her hair. Having been discovered by the Aether Paradise employees, she tried to give the Stufful back but it wouldn't let go.
Bewear showed up and recognized the Stufful as family and took it back with it.