The two Brothers—the gods of our worlds—basically made him immortal because they gave him a task. Every time he dies, his soul leaves his body and ends up in another person's body. So, that person, no matter how old they are, ends up with two souls at the same time.

Until, well, there's only one soul left.

[ That's what she's understood about Oz, anyway. Because sometimes it's hard to tell who's who anymore. Sad as it is, she thinks those souls become one in the end. Ozpin was just one soul... ]