When a person is "in a coma," he or she is conscious but is non-responsive. The person is alive but the brain is at a low-level of alertness.
Sometimes people "come out of" a coma; sometimes they do not. Doctors can measure brain activity, thereby providing family members with information needed to determine whether life support should be continued.
In the case of Elizabeth King, in The Descendants, the King family did not make the decision to remove life support. Mrs. King made that call herself, in a "Living Will," which directed how her medical care should be managed if she were ever severely injured.
The Living Will, among other things, set forth Elizabeth's "right to die" if her vital signs indicated that she was in a persistent vegetative state.
This image - from a 1990 TIME Magazine cover - depicts a father struggling with the difficult issues arising from the care of his comatose daughter.
Click on the image for a better view.
Image of TIME Magazine cover, online via TIME Magazine. Copyright, TIME Magazine, all rights reserved. Provided here as fair use for educational purposes.