What silent understanding do you think passed between Liesel and the mayor's wife? Why do you suppose Ilse Hermann allowed Liesel to browse through her library?

I think the understanding was that Liesel was allowed to take any book she wanted from the library. When the Mayor's wife, Ilse, sees Liesel steal The Shoulder Shrug, she becomes intrigued by the Liesel and invites her into her library. Ilse would leave the window to the library open for Liesel to climb in. Ilse suffered from the loss of her only son and Liesel seemed a distraction, even a new maternal interest. Liesel gave her a reason to connect with other people.