这里的finished“完成了，结束了”是形容词作表语，是由动词finish的过去分词变化而来。主语可以是人，但无被动意思。请看词典解释：

1.《牛津高阶》

finished  adj.

[pred 作表语] ~ (with sb/sth) (infml 口) in a state of having completed sth or no longer dealing with sb/sth 完成某事物; 不再与某人[某事物]有联系: 

I won't be finished for another hour. 我还有一个小时才能完事.

I'm not finished with you yet. 我和你还有事未完.

2.《韦氏高阶》

finished  adj.

a not used before a noun : having reached the end of an activity, job, etc.完成了，结束了。

He started his homework two hours ago and he still isn't finished.他两个小时前就开始做作业，现在还没有完成。

I'll wait here until you're finished.我就在这儿一直等到你做完。