Such bodies stay alive as long as there is a soul within. A live body, or rather, a body with a soul is described here as a Jiva. Jivas are categorized in two groups. Liberated Jiva or Siddha. Non-liberated Jiva or Sansari Jiva.
Liberated souls have no karmas and therefore, they are no longer in the cycle of birth and death.
They do not live among us, but reside at the uppermost part of this universe called Siddhashila. They are formless and shapeless, have perfect knowledge and perception, and have infinite vigor and bliss. All siddhas are equal and there is no difference in their status. They experience happiness and pain and have passions, which in turn cause the soul to wandering more. Except for the jiva of Arihants, non-liberated jivas have limited knowledge and perception.