Ms. von Furstenberg says that the moment that most defines her life is when her mother, Lily Nahmias, a Jewish Greek immigrant working for the Belgium resistance, was liberated from the death camp when the war ended in 1945.

After 13 months in Auschwitz and Ravensbrück, the 22-year-old was barely the weight of her bones, down to 29 kilos, with blue tattooed numbers, 5199, on her left arm. She had to be fed every few moments like a bird. A year later, she was married to her fiancée, a Jewish Bessarabian immigrant named Leon Halfin, who was in electronics and later the semiconductor business. Against her doctor’s warning that she couldn’t have a normal baby, she had Diane.

“And I’m not normal,” Ms. von Furstenberg said with a smile.

Her mother was tough on her, saying, “Fear is not an option” and “Don’t be a victim.” When the little girl was scared of the dark, her mother locked her in a dark closet to face her fear.

“Today she could go to jail for it,” Ms. von Furstenberg says in the documentary. “But she was right.” Her mother wanted to “equip” her in case she ever had to go through a trauma like she had.

That ability to look terrible news in the eye held Ms. von Furstenberg in good stead when, at 47, she got cancer at the base of the tongue. The key, she told me, is “not be a victim, not be angry, not say ‘Why me?’ Just say, ‘This is what my situation is. This is what the doctor can do. This is what I can do.’”

In the 80s, when Ms. von Furstenberg’s business was cratering, her mother, who had left her father for another man, went with her new partner on a business trip to Germany. Hearing a bunch of men talking loudly in German in the hotel sent her into a panic, and she was found crouching under the concierge desk.