Interestingly what a "cancer survivor" is, is not as straightforward as one might think.

Everyone has some cancer risk throughout their entire life, but people who've already had malignant cancer once are even more at risk, both for recurrence and new cancers. This is not just because the cancer may not have been completely eradicated, or that the person has shown a genetic predisposition for cancer; in addition to those factors, most cancer treatments (radiation and chemotherapy) can cause cancer!  

Because a person may die of cancer long after initial diagnoses, in order to meaningfully talk about cancer survival doctor's need to draw an arbitrary line somewhere: currently most studies concentrate on five year survival rates. That means if you live more than five years from initial diagnoses, you are generally considered a cancer survivor, even if you eventually die of cancer.

One might be tempted to use the phrase "cancer survivor" to describe anyone who has had malignant cancer and is currently alive or who didn't die of cancer. That may be okay for casual conversation, but such a term is useless in meaningful discussion. It requires waiting until all patients are dead to draw conclusions about whether they "survived." cancer in the end (I'm not interested in waiting that long to discuss effectiveness of current treatments), or it represents a moving (therefore ambigous) target while patients are still alive. And what about people dying of cancer who are hit by a bus?: with the casual definition such people are considered "cancer survivors", and being hit by a bus is an effective treatment for cancer since it produces more "cancer survivors" then is found among those not hit by buses. I suppose being hit by a bus is an effective treatment for cancer from a certain point of view, but that hardly represents meaningful information about cancer survival.

Really the word "survivor" in any context implies an arbitrary designation is being made: since we all die, none of us are survivors of any kind (unless some arbitrary distinction is made based on length of life).