It is never healthy to lose weight that rapidly.
The body only loses fat by burning it. That is only way that fat can leave the body. It isn't flushed away and it doesn't magically disappear.
Depending on age, height, activity level etc, the average person burns around 2,000 calories a day. Let's say these people even exercise like mad, and burn on average 2,500 calories a day!
But you gotta eat. So it's not all stored fat. Even this plan sounds like they don't ask you not to eat.
So let's say they eat very little. Healthy fruit and veg only, not much else, and topping out at an unhealthy low of only 500 calories per day.
So with a very generous rough guide to burn, and an extremely low allowance on intake, they're burning at most 2,000 calories of fat a day.
That's 4 pounds a week.
So what's the rest of the weight?
These are all things you want to keep! But that your body won't keep if you under-feed it with a fad diet. They're calorie-expensive to maintain, so the body drops them.
You know the body can't burn more than about 4lb a week in fat alone - so any claims of any greater losses than that should always be treated with extreme scepticism. That's not "fat" they're losing.
Deb, in New Zealand