Probably one of the best questions I've seen asked on SW ever. I think when life throws adversity at us, we are faced with a choice. I actually don't like your two examples much (rape vs cancer) because these are very different things to deal with emotionally, physically, psychologically, sociologically, etc.
But I think your bigger question is why do people react so differently when faced with adversity. Why do some choose to stand up and push through and others get so beaten down. Surely, a big factor is the type of assault. In your question, you mentioned cancer. Cancer is certainly an enormous physical assault typically tearing apart a person's body from the inside, but it is not a sociological assault. Quite the contrary, family and friends typically rally around cancer patients. Rape is a very different kind of assault and while the immediate physical act might not do damage to the extent of a full blown stage 4 cancer, it does assault the victim in so many more ways.
There are many other factors that go into how we react to adversity. Certainly our prior life experience, our belief system, our support systems, all of these and more go into it.
As for your friend in school... She may be damaged, but she is not broken. Please give her a hug from me. And maybe another one tomorrow. And the next day. Be kind to her. Make her feel human.
