After the Adversary took over all the Fables homelands, a group of surviving Fables fled to New York City in the mundane world and founded a new community, named Fable Town.
An amnesty was declared for all past crimes, allowing the much hated and feared Big Bad Wolf, now calling himself Bigby Wolf, to be made the new sheriff of Fable Town.
Bigby can change between human form, wolf form and a form that's somewhere in between, resembling a werewolf.
Like a real werewolf he is pretty much immune to most sorts of damage, but he is also somewhat susceptible to silver bullets. As with all Fables, his regenerative power/immunity is dependent on the amount his stories are told and remembered by normal people. A Fable known by everyone in the Mundy world becomes practically immortal.