For a patient to be on their "death bed" it signifies that nothing can be medically done to prevent the completion of their process of death. When nothing can be medically done to prevent such completion, why do you think that health care professionals are to be expected to pull a rabbit out of their hat or do some type of magic trick to prevent the completion of such process?
"demand and receive all life saving treatments" : again when a patient is on their "death bed" it is because all attempts relying on all possible life saving treatments.
You keep avoiding the question by assuming the problem away. Let's take this hypothetical:
Jacques has been given a diagnosis of advanced cancer an told he has two months to live. While reading about his disease on free government broadband, he sees an article about the Sultan of Brunei paying $20,000,000 to receive an experimental treatment in japan for the exact same disease that extended his life by a year. Jacques asks his doctor for the treatment. What happens next?
A) the French taxpayer foots the $20,000,000 bill to send Jacques to Japan and he gets the treatment
B) the French taxpayer pays for Jacques to get some painkillers and a bed in which to die
Who makes this decision?