I've heard of primitive cultures that believed that twins would share the same soul, and that if one of them died, the other had to be put down. No clue if anyone ever actually really did that, though.
Now, personally, I figure that a cloned person would have a brand new soul. (If you don't believe in the soul, that's a point for another debate.) However, mind uploading
renders that question effectively moot to all but the philosophers and theologists, because once we have the capability for both, we do have a way to make people effectively immortal.
I've heard at least one guy
predict mind uploading as soon as the 2030s, so we'll see how accurate that is. Once you have both, though, you have what appears to be effective immortality. A chip in the brain can make constant copies of a person's consciousness, and if you perfectly match both the mind and the body, you can consider it effectively identical unless you also believe in a soul. The only differences would be how much the body changes when you clone a new young adult with the scanned brain of a much older person.