It is a difficult one. Ive been a nurse and seen it from many persepectives. For the most part I think no, i dont agree with it, esp the way the OP presented it, it def should NOT be left up to the relatives.
I dont agree with doctors extending lives and causing suffering when there is no hope, i have nursed so many people who have ended up being PEG (tube) fed, having huge bed sores, in massive amounts of pain and really unaware of who is who and why we keep inflicting pain on them, I often thought, the kinder thing is just to let them go, rather than performing more and more interventions.
Secondly, I ended uo being involved in a case where someone had gone to Sweden for euthanatisa (where its legal) and the police got involved. I forget what he had as i was just a student back then, he had all his "wits" about him, he knew what he wanted, but he had no control over his body, he was permentley in a wheelchair, his wife his carer along with caring for 4 children.
he couldnt move anything, he couldnt swollow and would frequently start chocking, he was terrified of his wife even leaving the room as he would start drowning on his own spit and couldnt swollow. It was terrible. We all knew he wanted to end it, we obviously expressed no opioions on it, but he did make it clear he wanted to die. He couldnt have done it himself, so at his wishes his wife took him to Sweden and ended it. I dont personally see the problem. I dont really agree with Suicide, but in the same situation I would have wanted it myself, but I am not sure i would have wanted my family to have that responsibility.
As for being just killing themsleves, for the most part its people who know they are going to get worse and are happy to live their lives to the fullest until they are no longer able, at which point they want to end it (most cases due to pain, suffering and burdens on family) but when they are that point they cant physically do it themselves.
I have always sat on the fence with regards ethuanaisa, because i dont agree with anyone ending their lives pre-maturally, but having seen the other side, i am sure i wouldnt want to live like that. My husband knows not to preserve my life, esp when there is little hope.
The other problem is we sort of do practice it, with the theraputic doses of morphine, when someone is dying anyway, very often we use huge doses of morphine to control the pain, knowing fully well that those doses will kill the patient, once huge doses are give respiration slows down and the pateient evetually passes. However thats the case with Cancer patients, and people feel that its unfair that cancer pateints get that sort of therapy whereas other conditions dont.
Where it is legal its only carried out when conditions are terminal and end stage.
As for being on life support, thats not classed as euthanisia, euthansia is an active action, doing something with the intention of killing someone, whereas switching off life support is different, i cant explain is very well, but doing something to not perserive life like switching off life support or not resusuating someone isnt an active action. Hope that makes sense.
So I sit on the fense, but I can see why some people do it, but i hope im never in that situation to inflict on someone or have to do it for someone. I also feel that is very open to abuse and that its safer for it to be illegal than to make it legal.