Final answer:
The question seems to relate to a narrative involving complex relationships and sacrifices made to save lives. However, without context about Frau Kügler or her actions, it is difficult to determine how she saved Gerda's life or the nature of her relationship with the girls in her care.
Step-by-step explanation:
From the provided excerpts, it appears that the question is about a scene from a play or narrative involving characters with complex relationships and circumstances affecting their decisions.
While no specific information about Frau Kügler is given in the excerpts, it appears that the narrative discusses themes of sacrifice, duty, and the lengths one may go to save the lives of those they care for.
Relationships based on genuine affection are explored, such as a nurse who sacrificed her own child's upbringing for the sake of a job, or Nora, who contemplates the legality and morality of her actions to save her husband's life.
Themes of affection, sacrifice, and duty are present, but without the specific context of Frau Kügler's actions, it's challenging to determine the nature of her relationship with the girls under her care or how she may have saved Gerda's life.
Affection between caretakers and those they are responsible for is a recurring motif, suggesting that such relationships in the narrative are complex and deeply human, often blurring the lines between professional obligations and personal feelings.