In some older versions of Persephone's story, she was a young woman, not a young girl, and instead of accidentally wandering away, she had gone deliberately adventuring, when she fell, or was lured, or was kidnapped into Hell. Here Persephone's adventurous spirit leads her into difficulty, instead of her being a passive victim of the wickedness of others. Her relationship with her mother gives her the courage to explore her world, and when events take a bad turn, their relationship gives her the strength to survive.
In a still older version, Persephone heard the despairing cries of the dead and chose freely to go into the Underworld to comfort them. Hades does not appear at all, in this version. Here Persephone's descent to hell illustrates inclusiveness for every being, whether in the Underworld or in our present one, and shows that mercy is integral to her nature.
In the most ancient layer of myth, Persephone's name means "She Who Destroys The Light." She was the powerful Goddess of the Underworld long before anyone knew of Hades. Like the Indian Kali, the Irish Morrigan, and the Sumerian Ereshkegal, she was the Goddess of Death.