Since matter is neither created nor destroyed, all Souls move from body to body. When a person dies, the soul immediately transfers to a new, unborn host.
While it is possible for personalities and memories of past lives to be retained within the soul through reincarnations, it is uncommon. Once a Soul is reincarnated, it is usually as a new slate.
The only two exceptions to this are the Phoenix and the Soul Stealer. These souls have their own personalities separate from the host body’s. These souls learn through each reincarnation and are able to adapt.