It seems to me that there are two possible ways to interpret how this spell relates to the soul of a dead creature:
Once a creature dies, its soul is beyond the control of this spell
By this interpretation, it would means that when the host body dies, the creature's soul behaves just like the soul of any creature who's died (presumably continuing on to its regularly scheduled afterlife).
If the host body dies while you’re in it, the creature dies,
Note that this is explicitly distinguishing between the body dying and the creature dying. Given that the body is already dead, if the soul remained trapped in the container after the body died, what would "the creature dies" even mean in this case?
After a creature dies, its soul is still under the control of this spell
By this interpretation, then presumably both the caster and the target's souls would still be affected by the spell.
If the host body dies while you're in it, [...] make a Charisma saving throw against your own spellcasting DC. On a success, you return to the container if it is within 100 feet of you. Otherwise, you die.
The wording here is pretty similar to the description of what happens to the target creature: if you fail your save, you die. It doesn't say anything about your soul leaving the host body; it only says that you die.
The only conditions the spell mentions for your soul leaving the host body are if:
- You use your action to return to the container
- You succeed at your saving throw when the host body dies
- The container is destroyed
- The spell ends
If you're dead, you can no longer take actions. If you failed your saving throw, that only leaves the end of the spell or the destruction of the container.
If the host's soul is permanently trapped in the container, then the same is true about the caster's soul and the host's dead body. Your soul is now trapped in the corpse of the host for as long as the host's soul is trapped in your container.