In most cases, broken pieces may not be useful any more. The pieces are thrown away and a new one brought home.
That’s, if it’s a necessity and the means to replace it, is availabe. In some rare cases, what’s broken can’t be thrown away because a new one isn’t available.
So, the pieces are gathered, carefully, so that one tiny piece is not missed or lost completely. If one piece is not there, then mending what’s broken, becomes puzzling.
Every difficult puzzling problem requires the presence of a tiny piece of detail, often overlooked, for it to be solved. So when you are faced with a difficult problem, leave no stone unturned.