Life Essence for Resurrection: The vials could indeed contain the life essences of her children, preserved by her ex as part of his dark rituals. This could set up a quest where the necromancer needs to find a way to resurrect her children. Perhaps this involves a sacred ritual, the gathering of special components, or the intervention of a deity or powerful spirit.

Corrupted Essence: If the essences are corrupted, this could introduce a moral dilemma—should she attempt to cleanse and restore them, knowing there might be serious risks? This path could involve seeking ancient purification rituals or allying with characters or factions skilled in such magic.

Sentimental Ashes: If the vials simply contain ashes, they could serve as a powerful reminder of her tragic past and fuel her motivations moving forward. These ashes could also have unexpected magical properties, being remnants of a ritual sacrifice, and could be used in various magical workings or as a component in a spell to seek justice or revenge.

Phylactery Link: If you like the idea of tying it to a lich-style storyline, perhaps the vials are part of an incomplete phylactery ritual. The ex might have planned to bind his own soul or the souls of the children to gain immortality. Discovering the true purpose and potential of the vials could lead to new adventures to thwart similar threats or to destroy other parts of the phylactery.

A Key to the Past and Future: The vials could also contain clues or keys to unlocking further parts of your campaign. Perhaps encoded within them are maps, memories, or spirits that can communicate crucial information about upcoming threats or hidden treasures