What if a critical injured patient doesn't want to live anymore?

Lets say a patient survived a horrible accident that either caused them to become paralyzed, become terribly disfigured or lose a limb or more.

The patient really doesn't want to live with that quality of life. They are literally begging the doctors to please euthanize him/her, to please let them die. What happens in those cases?

What if a critical injured patient doesn't want to live anymore?
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