How does Max Vandenburg's life give Liesel purpose in The Book Thief?
In The Book Thief, Liesel relates to Max because they are in similar situations. Both have left (or been left by) their families to live with the Hubermanns. Liesel is Max's link to the outside world. He looks forward to their conversations in the basement. After a soccer game in which Liesel beat Rudy's team 6-1, Max asks her to describe the weather, a description "only a child could have given" (249).
Together, they bond through the creative process when they white out Hitler's Mein Kampfand make into an art project. Max needs these kinds of projects to occupy his time and mind. When Max gets sick, Liesel is always looking for presents to lift his spirits. Just as Max has "projects" to keep him busy, Max is, in a sense, one of Liesel's projects.
Also, Max was in hiding because he was Jewish. Liesel was hiding with the Hubermanns because her mother was the wife of a communist. They are both allies in the struggle against the Nazis. Shortly before Max leaves, the Nazis comes through town, herding Jews out. Liesel feels helpless as she watches. "She could only hope they could read the depth of sorrow in her face, to recognize that it was true, and not fleeting" (392). When Liesel talked to Max, worked on projects, and cared for him when he was sick, she did not feel powerless. She was doing something, hidden, but in opposition and defiance of the tyranny of the Nazis.