In The Book Thief, how does Death's self-revelation in part six explain his fascination with Liesel?

Liesel provides Death with distraction and moments of beauty.

Death is haunted by humans.  In this chapter, we learn a little more about why.  He explains that he is not the stereotypical image of the bringer of death that we picture, like the Grim Reaper.  He is a more complex presence.  Death doesn't bring death, he cleans up after it.  He also never gets time off, and has to see sadness and pain everywhere.  The reader feels sorry for Death, rather than being afraid of him!

They keep triggering inside me. They harass my memory. I see them tall in their heaps, all mounted on top of each other. There is air like plastic, a horizon like setting glue. There are skies manufactured by people, punctured and leaking, and there are soft, coal-colored clouds, beating like black hearts. (Part 6, Ch. 41)

Death worries about the “leftover humans.”  He has to face humans in their last moments, or after their last moments, all of the time.  Yet some of them stick with him.  Death tries to focus on colors, taking little micro-vacations in the beauty around him, but it doesn’t always work.

In Liesel, Death finds these “strewn pieces of beauty.” 

She’s carrying some snow down to a basement, of all places. Handfuls of frosty water can make almost anyone smile, but it cannot make them forget. (Part 6, Ch. 41)

Liesel is clever, compassionate, and troubled.  She is haunted by death, just as Death is haunted by her.  From the moment Death comes for her brother, the two are linked.  Liesel captures Death’s imagination and her attention.  He finds a vacation in her, because she is a beautiful person.  He reviews the moments of her life and enjoys watching her as if he is her friend.

In Liesel, Death sees one of his leftover humans.  She saw her brother die, and Death was there.  Yet Liesel makes the best of some really bad situations.  In Nazi Germany, suffering is everywhere.  Liesel is a bright spot in the darkness.

In The Book Thief, why is Liesel's life fascinating to Death?

In The Book Thief by Markus Zusak, Death describes himself as extremely overworked and weary of the things he has seen humanity do to themselves. Death is fascinated with Liesel, the protagonist of The Book Thief, because she continues to live and to celebrate life and freedom in others, even loving other people despite her circumstances. To say that Liesel is living in dire circumstances would be an understatement. When Liesel is introduced in the novel, she has been put on a train in Germany to travel to a small town close to Munich in the winter of 1939. Her father has disappeared. Her brother dies of illness and exposure on the train, and her mother disappears, leaving Liesel to bury her brother. She does not want to trust anyone but gradually learns to trust her foster parents, Hans and Rosa; Max, a friend of the family; and Rudy, a neighbor boy. Despite her enormous grief and loss, Liesel learns to read and write and begins writing her own novel. Everyone that she loves (except Max, who is conscripted into the army) is killed in an explosion. Yet, Death tells the reader that Liesel leads a happy life full of love, memories, and family. Through her enormous pain and loss, Liesel represents a triumph of the human spirit, an ability to recover from trauma and a will to live that fascinates Death.