Does a right to live imply a right to die?

Question comes from a program on the radio about India and whether or not the Jains have a right to starve themselves to death if they choose to do so. I believe the practice is called Santhara or Sallekhana and it involves choosing the time and manner of ones own demise.

Is there an implication that if you can choose to live then you can also choose when to cease living? What are the arguments, pro and con?