Abigail has incurable lung cancer. Her lungs no longer have the capacity to function without the aid of a respirator. She wants to be sedated and to have her respirator turned off. What has Abigail requested?

Abigail has requested what is called euthanasia.

Explanation:

Euthanasia is the practice of allowing someone to die if they are very sick or suffering. It can involve intentionally giving someone something to assist in their death like tranquilizers so they are sedated and then withdrawing a treatment or equipment that is keeping them alive, like the respirator mentioned in the question example. It is a controversial practice with those who are opposed outright because it entails human intervention in deciding who should live or die and those who think it is the most humane thing we can do for the terminally ill who are experiencing pain.