Some good news here.
It’s good to remind ourselves that being pro-life and Christian doesn’t necessarily mean insisting that futile treatment be given to a dying person who has no chance of recovery. As the Catechism says:
2278 Discontinuing medical procedures that are burdensome, dangerous, extraordinary, or disproportionate to the expected outcome can be legitimate; it is the refusal of “over-zealous” treatment. Here one does not will to cause death; one’s inability to impede it is merely accepted. The decisions should be made by the patient if he is competent and able or, if not, by those legally entitled to act for the patient, whose reasonable will and legitimate interests must always be respected.
But also this:
2279 Even if death is thought imminent, the ordinary care owed to a sick person cannot be legitimately interrupted. The use of painkillers to alleviate the sufferings of the dying, even at the risk of shortening their days, can be morally in conformity with human dignity if death is not willed as either an end or a means, but only foreseen and tolerated as inevitable. Palliative care is a special form of disinterested charity. As such it should be encouraged.
What’s the difference between paragraph 2278 and euthanasia, aside from intent? There’s a very practical difference. In paragraph 2278, if the patient continues to live when a treatment is discontinued, then you allow the patient to keep living until natural death ensues. In euthanasia, you don’t let the patient live, but rather take a concrete action to make sure the patient dies.