The Continuous Katherine Mortenhoe by D G Compton

A few years in the future, medical science has advanced to the point where it is practically unheard of for people to die of any cause except old-age. The few exceptions provide the fodder for a new kind of television show for avid audiences who lap up the experience of watching someone else's dying weeks. So when Katherine Mortenhoe is told that she has about four weeks to live she knows it's not just her life she's about to lose, but her privacy as well.