In Bleach, Soul Society represents this sort of Heaven where souls are sent by Shinigamis (mostly from Earth?). However, once in Soul Society, is a soul immortal? Can they die? And if so, what happens? Is one sent to... Hueco Mundo?
From the Bleach Wiki:
The Human World and Soul Society are parallel to each other and are two sides of the same coin. Families separated by death are rarely reunited in the Soul Society unless they arrive in Soul Society together. People live nestled together like a family of strangers. One never gets hungry (if she or he doesn't have spiritual powers) and aging is slowed to a great extent, with lifespans of 2000 or more years not being unheard of, though such ages are limited to Shinigami or other Soul Society dwellers with high spiritual power.
and to answer your question,
A soul that dies in Soul Society is reincarnated on Earth as a new Human with no past memories.
Edit: However, given the huge difference in lifespan, Soul Society should accumulate souls and the Human World should run out of souls...
souls can "escape" this cycle by turning into hollows and entering Hueco Mundo (or god knows which new worlds Bleach will come up with). Souls can be exterminated permanently by Quincy:
Quincy completely extinguish Hollows. Thus the souls that come to the Human World do not return to Soul Society and therefore the souls would increase only on the side of the Human World. Meaning, the Human World becomes heavy in souls causing Soul Society to spill over into it; mixing life and death. The ultimate result would be the end of the world.