castoff
Something unwanted that someone has thrown away or given away.
A castoff is something that someone has thrown away or gotten rid of because they no longer want it or need it. When your older cousin outgrows her shoes and passes them down to you, those shoes are castoffs. When a family donates old furniture to a thrift store, those items become castoffs looking for new owners.
The word often suggests that something still has value or usefulness, even though the original owner doesn't want it anymore. Libraries sell castoff books at fundraisers. Younger siblings often wear castoff clothing from their older brothers and sisters. A theater might use castoff furniture as props in its plays.
Sometimes people use the word to describe feeling rejected or unwanted themselves, like a team member who feels like a castoff after being left out of an important game. This usage suggests hurt feelings, because nobody likes feeling discarded.
In everyday language, it simply means something set aside or rejected, whether that's an old jacket, a broken chair, or even a person who feels left behind.