I think a person has the right to choose euthanasia. If you're unconscious, others can make such decision on your behalf. So, if you want them to make the right decision, make sure you have a living will on file at the hospital.

What about when the one has a care plan that explicitly states the will to continue living as long as possible? Should a hospital be able to claim that person's a drag on resources and therefore should have life support services discontinued in contradiction to what their care plan states?

If there is a care plan then going against it should require the hospital to convince a judge to issue a court order to discontinue life support. So the hospital would have to prove that discontinuing life support is in the patient's best interest and not just the hospital's best interest.

"So the hospital would have to prove that discontinuing life support is in the patient's best interest..."
Isn't that just a little scary to you? If I've explicitly said how I want to be treated in an event that incapacitates me, who should have the right to change that? Or in the case of a child, as in the recent cases in England, shouldn't the parents or a patient get to decide if they want to try a risky or expensive procedure? I get that a hospital could refuse to do a procedure because of liability or something along those lines. That's not what I'm talking about. I mean when all of the pieces are in place except that a judge decides it's not in the "patient's best interest". That just doesn't seem like a good idea to me. It's too easy to abuse. I think it's best to leave that power in the hands of the individual.