What were the responsibilities of Persephone?

Queen of the Underworld

Passage to a blessed afterlife in Elysium (by Persephone and Demeter)

Hades and Persephone presided over the oracles of the dead and the art of necromancy (nekromankia), the summoning of the ghosts of the dead.

Persephone was the queen of the Erinyes, underworld daimones who punished the crimes of filial betrayal, impiety and murder. She dispatched them from the Underworld when curses were invoked in her name.

Persephone was the goddess of spring growth, and more specifically of the grain crop. Earth flourished when she returned each spring from the underworld.