Having been
后面是过去时 所以前面要用现在完成时
而这个完成时要做主语 所以要用完成时的名词形式
也就是 Having been

out of work
[英][aut ɔv wə:k][美][aʊt ʌv wɚk]
失业;
例句:
1.
Holiday gatherings can be anything but festive for people who are out of work.
对于搜趣网失业的人来说，节假日聚会根本不是什么快乐的场合。
2.
Millions have been thrown out of work.
已经有上百万人失去了工作。
3.
He invented an advanced sewing machine, but feared it would throw seamstresses out of work.
他还发明了先进的缝纫机，但又害怕这会抢了裁缝的饭碗。
4.
With so many people out of work, every job has a lot of competition.
失业的人如此多，所以每一份工作都有着很大的竞争力。
5.
Over the summer, more than half of under 25-year-AHzAkXolds in spain and greece were jobless, while the segment of people out of work in the euro zone as a whole reached a 15-year high at 17.2 million.搜趣网
与此同时，欧元区25岁以下失业总人数达到了1,720万人，创下了15年来的峰值。

work on sth.就有“直接平面接触”地作用于宾语，具体地改变宾语的状态的意思；
而work at sth.就没有那么具体直接，它只表示“点存搜趣网在”，
work at 从事，致力于……
work for 为……做事，为……尽力，被……雇佣者
work out 可以解决，设计出，算出，计算出，消耗完
挤出去
work in 引进，配合
work as 作为....的工作

out of work 正确
祝你学习进步，更上一层楼！ (*^__^*)
不明白的再问哟，请及时采纳，多谢！