The first solution in Number the Stars is that Annemarie overcame her fear.  When needed, she was filled with courage.  In a conversation with Uncle Henrik, he asked Annemarie if she was brave.  She replied that she was "not very" brave.  Her uncle reassured her.  Later, Annemarie had to walk alone on the path to the water to deliver the package to Uncle Henrik.  On the way, she was encountered by Nazi soldiers with dogs.  They interrogated her and she was frightened.  She managed to have enough courage to say the right things to the soldiers so they would let her go.

Another solution is that Ellen and her family were able to escape.  Their escape was carefully planned, and there were several close calls that almost prevented it from happening.  In the end, they sailed across the water to freedom in Sweden.

Last, Ellen and her family still had their pride.  They had lost so much.  They had to leave behind their home and possessions.  But despite their difficulties and sacrifices, they had kept their pride.  This was noted as such:

...their shoulders were as straight as they had been in the past: in the classroom, on the stage, at the Sabbath table. So there were other sources, too, of pride, and they had not left everything behind.