I'm Catholic. I believe humans have souls. Let's start from there.
Medicine and technology are growing increasingly sophisticated. As parts of the human body wear out or sustain damage, they can be replaced with artificial components. The augmented human body will be added to and tweaked until it runs indefinitely. At that point we may discover souls have a limited earth life span.
So the body keeps going, but the soul has gone. What would this mean in practice? Would we notice the absence of soul? Is a person still human without a soul? still a citizen? Would their needs and desires change without a soul? Would society/government prefer a soulless body and what research would have to be done to learn how to kill the soul but not the body?
But what if it went the other way. What if the augmented body parts became wrapped in soul? Such parts don't die. Would they hold the soul on earth? Would they have to be ritually burned? Would a used body part transfer soul to its next body?