Alot of times, the worthless that people are refering to, is normally tossed on the burn pile or literally thrown in the garbage.
An example is rotted/spalted wood. This is a very soft, punky material, that is almost impossible to work with, unless your timing is perfect. I have seen wood that, while it looked amazing with incredible colour and veining, you could crumble it in your hand. After stabilizing, it can be used for almost anything.
Another example is the live edge pieces that get cut off boards. Quite often, when the bark is removed, there is not much wood left, maybe only 1/4"-1/2". Worthless, but when you mix it with some resin, you get some beautiful combinations.
I hope this helps.