Although im not sure myself
What could have happened was that after Oz's rabbit doll body crumbled in the arms of jack, oz's soul would have remained in the abys and since Oz achieved his task of delivering the memory to jack in other words granting the Will of the abby's wish, she returned the favor by turning Oz into a chain, giving him a new body
I.E. B rabbit then, jack made a contract with B,rabbit Oz, now heres what i think might have happened its a bit tricky but hopefully it will answer the question.
When jack released 'B.rabbit Oz' to fight the baskevilles (and oswald/Glen) The tragety of sabrie accured swallowing everyone into the abys although jack is presumed dead, his soul still resides in his body but he is just sleeping/unconsious (but later, as you know he regains control of his own body), the same goes to Oswald/Glen.
Anyway as jack was contracted to B.rabbit, who's soul resides within the body of the contractor,until it is released, (remember when Alice contracted Oz,after the KISS she possessed his body in order to escape the abbys),this ability may have been used in order to claim jack's body
Jack's soul is still in the body but is rather weakened giving B.rabbit the advantage to posses/control the body but since they are in the abys, time differentiates meaning jack was born again 85 years later but instead, he was actually the B,rabbit (after coming out of the abys, he will have no memory of himslef, jack or the tradgety, the same goes for Gil and Alice when they came out of the abys having no memory of before) he is then named Oz and so the chain believed he was Oz vessalius and so foruth abit confusing but it can happen.