The liver will still have to produce ketone bodies, because fatty acids can’t cross the blood-brain barrier; only β-hydroxybutyrate can, and if you’re not eating carbohydrate, there’s not enough glucose (the red blood cells have no mitochondria, so they and certain other cells need the glucose the liver produces—and the brain loves β-hydroxybutyrate, that’s where the “keto clarity” comes from).
What happens to the excess fat beyond that is not clear, to me at least. Some of it can be wasted in various ways, since the body can ramp up the basal metabolic rate, and adipose tissue can metabolize fatty acids, if need be. I suppose really too much fat would end up being stored, since even fat stimulates insulin secretion to some degree, and enough insulin would push fat back into the adipose tissue . . . .
Of course, in real life, no one is likely to be able to eat that much fat. I suspect that, because fat is so calorie-dense, one would get awfully full and not be able to eat past that point. Case in point: I overate fat last night (not that much, but still), and today I am waiting to get hungry so I can eat. I want to eat, but I just can’t!