It is more like a futile care case as in the case of Andrea Clark and Mrs. Vo. But like with Terri, it is others making the decision to euthanize someone regardless of the wishes of close relatives.
It is totally unlike any of those cases. If the ventilator was removed, the child would die. Even the Catholic Church would not say there is a moral obligation to extend this child's life.
There are two sides to this question. The hospital has determined the person to already be deceased. (I assume)
The mother, naturally and understandably, does not.
Therefore, the term "euthanize" is already preloaded.
The other question is the one about who is to pay for the continued "life" support. Some think the hospital has the responsibility to continue to pay, for as long as the relatives desire. I am not one of them.