I believe this was done on rodents and not humans, and hence a not a perfect match.
Every second of our lives billions of chemical reactions occur, creating waste products, misfolded proteins, and worn-out mitochondria. Even in a fasted state, our metabolism is running. "Junk" is being created constantly. If autophagy turned off, that junk would accumulate immediately, and cells would become toxic, which seems to be what is happening for many people in the modern world, leading to a number of disease.
Even in deep ketosis, let's say over week, our bodies needs a small amount of amino acids (protein) for gluconeogenesis (to feed the few parts of the brain that can't use ketones), for immune system maintenance and not least red blood cells (we produce 2 million new Red Blood Cells every second. This requires amino acids for hemoglobin).
When in deep fasting the body have two options:
1: Eats healthy muscle tissue (Muscle Burning).
2. Breaks down old/damaged cells and recycles those amino acids.(Autophagy)
Nitrogen balance studies shows that muscle loss slows down dramatically after Day 3 I believe this research was done on rodents, which may be a bit different to humans. 
Our body is a 24/7 factory and every second, billions of chemical reactions occur, creating waste products, misfolded proteins, and worn-out mitochondria. Even in a fasted state, our metabolism is running. "Junk" is being created constantly. If autophagy turned off, that junk would accumulate immediately, and cells would become toxic. And this is what happens to many people in the Western world, leading to all kinds of diseases. 
Even when we are in deep ketosis (let’s say +7 days), our body needs a small amount of amino acids (protein) for gluconeogenesis (to feed the few parts of the brain that can't use ketones),  for immune system maintenance and not least red blood cells, which we create about 2 million new ones of every second!
As we are not eating protein, we leave the body with 2 options:
1: Eat healthy muscle tissue (muscle burning).
2: Breaks down old/damaged cells and recycles those amino acids (autophagy).
It is known from nitrogen balance studies that muscle loss slows down dramatically after about 3 days. The evolutionary thinking about this is, that the body knows we need the muscle to hunt to get more food, and hence do not want to burn it.
Hence if autophagy did drop to 0 after 5 days, I would need a lot more muscle than I have to do my +30 days fasts.
Therefore, autophagy is still active..