In Bans CaseBan's case, the Foxfox is Linkedlinked to his Sinsin of Greedgreed,because because he drank the fountain of youth. But iI guess in Japan, their Abilityability to heal comes from the Fox Demons called Kitsune wichwhich have a variety of powers.
And iI would guesguess the Wolveswolves' healing comes from the WerewolfesWerewolves Tales where they would heal any wound imidiatelyimmediately if it wasn't inflicted with a silver weapon.