In time, it became an accepted fact that the Cox brothers employed a conscientious ghost that did most of their work for them.
这里 that did mostof their work for them.
这里主语省略了吗，可以改成 that it did mostof their work for them.
或者省略掉 that，直接说成 the Cox brothers employed a conscientious ghost 吗？
the Cox brothers employed a conscientious ghost that did most of their work for them.
that did most of their work for them是定语从句。修饰ghost。that在乎义上指代ghost，并在从句作主语。
关系代词在定语从句中作主语，只有一下几种状况在非正式语体可以省略关系代词。
1 从句修饰there be句型中的真的主语时：
There is a man asks for you.
2 关系代词为there be句型中的真的主语：
I had to use anything there was.
3 This is the man wants to see you.
4 It is the man wants to see you.
其余状况都不可省略在定语从句中作主语的关系代词。
提问者的问题可能是没看出定语从句致使的。
句子剖析：
In time, it became an accepted fact that the Cox brothers employed a conscientious ghost that did most of their work for them.
in time: 时间状语
it：形式主语
became：系动词
an accepted fact: 表语
that the Cox brothers employed a conscientious ghost that did most of their work for them：真的主语从句
主语从句进一步剖析：
that：引导主语从句的从属连词
the Cox brothers: 主语
employed: 谓语
a conscientious ghost: 宾语
that did most of their work for them：定语从句修饰ghost. 其中that为主语，did为谓语，most of their work为宾语，for them为状语。
