Hopsinto wrote a terrific reply. The only thing I would add is to make it more specific.
Keeping the blood Sugar stable is crucial. Insulin is used to control many bodily functions, so fluctuations in insulin levels cause chaos in the metabolic system.
Juices from fruits, carrots, beets, and other "sweet juices", tend to cause blood Sugar to rise suddenly. Some of these juices are cleansing, but they contain more carbs/calories and are not good for Sugar sensitive individuals to drink in quantity.
Fiber and fats slow metabolism of sugars, but in juice you have none of those. A spike in sugar requires a steep rise in insulin production to normalize blood sugar levels. When this is accomplished, insulin levels fall. Juice is metabolised quickly, so this up/down will be within an hour. If one's insulin regulation is off, insulin is over produced, causing rebound hunger or worse, diabetic shock.
Juice from green veggies, purple cabbage, red bell peppers, tomatos, radish, parsely (and other herbs), cucumber, etc., don't have enough natural sugar to cause blood sugar spikes or a rise in insulin levels. Lemon, lime, garlic, ginger, horseradish, etc., are all healing additives and flavorings for these juices.
The carb/caloric content of most green juices is lower than that of fruit juice, but one must be careful not to overload on iron, oxalic acid, etc. They can be diluted with pure water to make them palatable.
A fast that would help someone gradually reduce calories in their juice intake might start with an apple/orange/carrot base juice and add 25% veggie juice the first day, 50% veggie juice the next day, 75% the next day and drink pure veggie juice starting the fourth day. I would dilute all the juice drinks 50/50 with pure water.