Shinigami no Ballad
Reading the synopsis, I couldn't help but be reminded of Shinigami no Ballad: Momo the girl god of death. That's an anime about a white shinigami who tries to ease the suffering of the people she encounters - she cries for the dead because they can't cry, she carries messages for the living, and she follows those who are going to die so that she can learn about them.
Anyway, that sounds vaguely familiar. Any suggestions/ideas/thoughts?