Afterlife

The Afterlife or the Underworld is the dimension or plain of existence where all living beings and animals go after their death. Though it has yet to be seen officially in the series itself, it has been mentioned and referenced several times by various characters, most notably Lala whenever she goes into a roleplay.

Current Inhabitants

 * Dullahans
 * Grim Reapers
 * Shinigami

Former Inhabitants

 * Death
 * Lala

Ways to Access the Afterlife
For most living beings, there is really only one way to enter the afterlife and that is their death. As Lala explains in Chapter 38, when a living being dies, only its body dies, but its soul is immortal and goes to the afterlife after its death. Apart from that, Dullahans and other psychopomps like Grim Reapers can walk between the worlds as "Herald of Death" and enter and leave the afterlife at any time of their own free will.

Ways to Leave the Afterlife
Usually death is final, but many times throughout the series, Kimihito has shown the unusual strength of facing death, despite the numerous near death experiences he had. As Lala explains in Chapter 30, that will is based on his caring for others, not on fear of his own death.

Apart from that, there is also the possibility for a living being to return as a Ghost in order to come into contact with the living, which is independent of whether they were Human or Liminal during their lifetime. However, the exact possibility with which one can become a ghost is unknown and it seems to be a very rare event anyway, presumably because most people accept their death and therefore do not want to return to the world of the living.

Wladislaus Drakulya appeared as a ghost after his death and took control of his daughter in order to use her as a means for his own ends. However, as Lala explains in Chapter 51, the dead have no right to do violence to the living, so she used her power as a Dullahan to sever Wladislaus connection to Curie, thereby severing his connection with the living world.

It's not known whether animals can also return as ghosts, but this presumably happens very rarely, as many animals don't have a higher level of consciousness and therefore do not have the will to return to the world of the living.