There is an interesting Halacha related to Succah that has Shabbat ramifications. It involves that which is permitted to be used for Schach.
We are forbidden to use any vessel on the roof of our Succah that is מקבל טומאה, that is susceptible to ritual impurity. This applies today, even though there are no laws of טומאה, applicable today.
The definition of a כלי, a vessel, is something that has a use, as in a receptacle. A wooden chair is an example of such a vessel. This means that one cannot use a wooden chair as Schach, because it is מקבל טומאה.
However, if a chair was broken into pieces, those wooden pieces, could be used as Schach, since they no longer constitute a vessel. The Shabbat laws work in a different manner. A chair, is not Muktza, and we are permitted to use it on Shabbat. But if the chair breaks, its fragments no longer have a purpose, and become Muktza, and may not be moved or carried.
Regarding Succot, the chair cannot be used as Schach, but it’s fragments are permitted for use. But regarding Shabbat, the chair has use, but it’s fragments do not. This is a confusing type of Halacha, as the same object, the chair, has different ramifications depending on the context it is used.