废柴 is Cantonese in origin (faai3 caai4) and entered Mandarin via Hong Kong pop culture. It's informal and often self-deprecating — friends can call each other 废柴 affectionately, but it's still an insult aimed at someone else.
memory
Literally 'waste firewood' — wood that can't even be burned. A cutting image: you're not just useless, you're useless at being useless.
