Regarding 'breaking a fast', that really depends on whether someone's following a so-called "water fast" or a simple caloric fast. If you're referring to ketosis, the only thing that can end that is intake of additional carbohydrates. Barring that, your body needs to break down fats (since the biological pathways to consume protein are extremely inefficient) to sustain your BMR, which isn't significantly correlated to current diet.
re: ketosis, the Wikipedia article is sufficient for a layman understanding, and the safety section illustrates why keto is not medically advised. re: fasting, this metastudy is a comprehensive overview of the current literature suggesting that intermittent fasting is beneficial to weight loss, though it establishes that this is due to fasting being a useful tool for caloric restriction, not popsci hypotheses involving ketosis or autophagy. Also note that some terminology surrounding fasting, e.g. "breaking" a fast, is fairly arbitrary depending on the speaker and arguably meaningless.