Damon has been terminally ill with multiple fractures to his skull. he has been in a vegetative state for over three years. finally, his family agrees to end his suffering by removing him from the life-support system. this is an example of euthanasia.

This is an example of passive euthanasia, in which a person isn't directly involved in killing someone, but indirectly allows them to die, mostly by taking them off of life-support systems or withholding them from further treatment. In Damon's case, his parents have no direct involvement in his death, but by taking him off life-support, they're allowing him to die, which makes it passive euthanasia.