Old thing

An “old thing” refers to relationship. When someone uses “old thing,” it’s typically because they have nostalgic sentiment for it. When someone says they want “the old thing back,” (which is the context it is used in majority of the time), it means that they want things to go back to the way they were before. They miss how things were between them and their ex. It is usually used when substantial time has passed between the present and the relationship they had with their ex, OR there has been a long period of time since things went south in their relationship with their ex.