As for rare items, I think looking back at the origin of materia will make this easier to explain. Materia are essentially the crystallized essence of gear, encompassing the history of an item and the person that used it. In the same vein, item desynthesis may result in something that encompasses the relation between an item and the person who crafted it. These crystallized objects will be a new material that you haven't seen before. And by combining these with a certain item that already exists, something interesting might happen, so please try it out. Also, even if you don't receive one of these crystallized items, item desynthesis is convenient for recovering ingredients to create things you need, so please try breaking down a variety of items. However, there is no guarantee that you'll obtain all of the materials that make up an item. If we were to make this possible, the game’s economy would collapse. The item you obtain and how much of that item are decided by your desynthesis skill and the item’s item level.