主语是 Theirs 用来替代 Their friendship,因为避免重复用同样的字眼。
也完全可以改写为 Their friendship was odd 语义相同。
后半句是用来说明主句的原因,being 不能省 (he 之后的已经被省了)。
用同样的句型:
Theirs is not a sound relationship being so far away from each other, she living in Beijing and he in New York.