Dr Mario Kart:
This is the first and only time I've ever laughed at one of those "cat pics with funky words under them" pictures... and I laughed long and hard. Congratulations.
I would also make the following observation: People, even with full-blown dementia/Alzheimer's/neurological disorders, are more likely to succumb to their fate if they feel relaxed, at peace. If the cat is curling up with the patient, even though they *say* the patient likely doesn't know the cat is there, the patient may still feel the cat on them, feel the warmth or *something*. If this is the case, it would certainly support the idea that when the cat curls up, it gives the patient some level of comfort, some feeling of companionship, that causes them to relax a bit and finally give in to their illness. Even if the person is completely unresponsive to external stimuli like talking or touching, doesn't necessarily mean they can't hear or feel what's going on. We don't know that for certain.
So really... the cat may almost be giving people the comfort to finally die, rather than predicting when it actually happens.