In all my many experiences with juice fasting, no, my skin has never sagged. The most weight I've lost at a pop was 30+ pounds in 30 days and I'm 40 something...
You are FEEDING the body with live juices while on your fast instead of starving the body with dead foods. The enzymes, nutrients, anutrients, vitamins, etc., feed the body down to the cellular level, so the skin is being fed from the inside out. Skin brushing is an excellent tool for the beautification of the skin and goes hand in hand with a juice fast.
Diets that starve the body with SAD foods will not prevent sagging skin if large amounts of weight have been lost in a short period of time. I have seen this happen with friends. I'm sure we all have at a time or another when our overweight pals go on crash diets or take diet pills for rapid weight loss. Yo yo dieting also creates sagging skin, especially if it's SAD yo yo-ing.
Juice fasting balances, heals, rebuilds, rejuvenates the entire body, including the skin.
There are a few articles on my blog that discuss rapid weight loss and the skin during a juice fast. Unfortunately I can't remember which ones... but here is a link where I compiled the best blogs on one page and you will find this information with a bit of looking... While you're there, check out the blogs that discuss the healing properties of specific veggies and fruits and use those that benefit the skin... such as the cruciferous veggies, cukes (did a great blog on the benefits of cucumber recently), melons and so on... drink skin veggies every day.
However, all that being said, there will be some people whose skin will sag, simply because of their particular circumstances and body chemistry. Such as persons who are a couple hundred pounds over weight and lose the weight rapidly, for example. But for the most part, on average, most people don't have the problem with sagging skin on a successful juice fast.