It's when nothing (more) can be done to help the patient. It's something I have to translate (French into English), and it doesn't apply to a human being, but to the earth, many years from now, when it's about to ... burst,...stop existing? ...disintegrate? In French, it's called "Phase terminale" (terminal step, phasis, condition) I don't think "incurable" will do the trick...
I think you were about right with your direct translation "terminal phase". If you wanted to be a bit colourful or use literary language, you could use "death throes" i.e. "the process of dying or ending in a very painful or unpleasant way"