My understanding is that the body will convert protein to Glucose when needed, but it is very carefully regulated, and will prefer ketones for cells that can run on them. However, some cells require glucose, and gluconeogenesis is important for that if you're eating low carb/in ketosis.

No citation, but If you think about it it makes sense: is you have no fat left, and aren't ingesting enough calories, your body would rather burn muscle than organs.