This is an interesting topic..is euthanasia acceptable in Buddhism.
Why we have to suffer in the first place is due to our negative karma..if we meet in an accident, or are in very critical states, where our body itself cannot heal, but our consciousness is still within our body, it would be a result of us having created the causes for ourselves to receive the same in this life. Therefore, karma wise, euthanasia would not be acceptable, because one would have to live out the extent of their karma, and experience it, before that karma is exhausted. If the person is euthanized, then in their next life, they would have to experience it again.
Also, for the family members, the pain and suffering they are going through, would also be a direct result of karma. Therefore they themselves would have to exhaust this karma by experiencing the effects of what is happening rather than avoid and cut it because it does come back.
On another thinking, if one would not have Dharma, euthanasia would be an option that would be frequently considered, because it is choosing to end misery, for both parties, to avoid having to go through suffering any longer, which is what samsara would always teach us, because ultimately, it is easier for ourselves..