Does fat physically leave your body when you lose weight? (see details!)

Recently, I read on a weightloss website that when you lose weight (and, hopefully reduce your body fat percentage) that the fat doesn’t actually leave your body. Instead, you’re just shrinking your fat cells. As well, the person who posted this information said that even if you have liposuction to remove some of those fat cells, they can come back if you don’t maintain your good eating and exercise habits.

Does anyone know if this is true? The person who posted this on the other site is neither doctor nor certified trainer, so I don’t know if her information is accurate.