your friend comes to school very upset

very upset在这里是主语的补语
very 作为副词修饰 upset
upset 在这里是形容词,意思为：伤心的、难过的、不开心等
这种用法英文比较常见,同宾语补足语一样,表示状态.
如：
he stayed there sad.
he died young.
she came home sick.
don't marry young.