Actually, very low fat diets such as the 80 10 10 diet are in a way not beneficial to the liver, because fat is needed to produce bile, which is the carrier for toxins the liver filters. Stagnant bile makes you also very prone to gallstones. If you detox without stimulating bile to be released, you're gonna feel awful.
But the good thing is that there is alternatives for bile production. Beet juice, turmeric, black radish are all great choleretic. So a fruitarian should use those on a daily basis for optimal liver health in my opinion.
Liver Flushing is beneficial, whatever you diet is. Fruitarians will tell you to eat fruits and let the body do the rest, but it is because very few of them know how the body actually works.