what caused Henrietta's malignant cells to survive and become applicable for medical research?
lawrencec

According to Wikipedia:

Doctors still have not discovered the reason for HeLa cells' unique vigor, but suspect that it is due to altered telomerase function. There are almost 11,000 patents involving HeLa cells

Henrietta had that one in a billion mutation in her cells that was very fortuitously was found. Actually, many of the medicines used today happened by shear luck in the hands of a prepared mind.

There's a great book about the serendipity of many medical discoveries called "Happy Accidents" - http://www.bookbrowse.com/reviews/index.cfm/book_number/1957/happy-accidents which illustrates many examples relating to dianel's comment - as Churchill apparently said, "Men occasionally stumble across the truth, but most of them pick themselves up and hurry off as if nothing has happened." - as the book jacket blurb for this book says, "within the scientific community, a certain stigma is attached to chance discovery because it is wrongly seen as pure luck. Happy accidents happen every day, but it takes intelligence, insight, and creativity to recognize a 'Eureka, I found what I wasn’t looking for!' moment and know what to do next."