I guess like legally speaking, kids are property of their parents. But in cases of current or impending brain death, shouldn't some kind of 'ward of the state' status kick in?
in cases of parental neglect of dying children, it's the stupidity of the parents that eliminates any chance for the child to recover (e.g. faith healing of childhood cancer)
in the case of a child that's already terminally ill and dying anyway with no chance of recovery, there's zero potential for recovery and the decision should fall on the individual first and foremost, but if they're unable to consent (let's just say the legal age of consent for medically assisted Self Delete is the same as for love, so 16 in most places), then a parent/guardian has to make the decision. The individual, even if they can't consent, should have veto power if applicable though. In other words, they can't explicitly say "yes, kill me" but a parent/guardian can't force them into medically assisted Self Delete either