What your are describing is a protein sparing modified fast (PSMF) and there are many versions easily found on the internet. A PSMF puts the body in ketosis, i.e. using fat for fuel. Yet the consumption of a small amount of protein allows the person to continue maintain and build strength with anaerobic exercise. This is why PSMF is often used by bodybuilders and athletes.
the first few days of a fast can be brutal as your body shifts from using glucose as a fuel source to using fat (ketosis) there is slight muscle loss in this initial phase. Expect aches, pain, nausea, dizziness, headaches, etc... A lot depends on how toxic the body is and underlining health issues.
It is recommended for water fasters to limit exercise yet many find that light walking or swimming and stretching helps the body flush out the toxins, thus easing the detox symptoms.