In Hinduism, we believe that when a body dies, the soul goes up and then takes (re?) birth. The (re?) birth could be of anything. Say, if I die, depending upon my sins and meritorious deeds, I'll take birth as an insect, fish, dog or even a human.
Hindu sages and gurus have specified the ultimate solution to get rid of the cycle of rebirths. It is called as the Moksha The soul is then with god and free from taking any birth. That's it. The story is finished. This makes the soul divine and free from joys and sorrows. This was an ultimate goal of those sages then.
Wikipedia explains it in a sentence using some words but still does not define one term.
I'm not sure whether this theory exists in any religion, and thus may not get the exact term but in English, anything close to this will work.