我认为what to be done是不正确的。

疑问词+to do不定式本质上是wh-疑问词引导的名词性从句的简略形式。当从句的主语在主句中已经出现（通常为句子的主语或宾语），并且从句的谓语是主句谓语时间之后的将来动作，则wh-从句省略主语，同时谓语形式改为to do不定式。例如：

I don't know where I should put the book. = I don't know where to put the book.

I told him what he should do.= I told him what to do.

反过来，疑问词+to do也可以还原成wh-词引导的名词性从句：用主句的主语或宾语作从句的主语，不定式改为情态动词结构。例如：

Please tell me how to do it. = Please tell me how I can do it.

I haven't decided where to go for the holiday. = I haven't decided where I will go for the holiday.

I can't decide what should be done. 这个名词性从句中的成分没有在主句出现过，不能简略为疑问词+不定式结构。

以上内容系根据语法原理进行的推测。供参考并期待指正。

这种情况类似于介词+which+to do作定语，实际是定语从句的简略形式，可以还原为定语从句。

I need a sheet of paper on which I will write a note.

= I need a sheet of paper on which to write a note.

反之亦然：

He wants to build a new house in which to live.

= He wants to build a new house in which he will live.

补充内容：

间接问句（即由一般问句、选择问句或特殊问句转变而来的名词性从句）的使用受句子谓语动词、形容词、或介词的制约，不是可以任意使用的。例如，我们可以说I forget whether Tom was present. 但不能说 I regret whether Tom was present.换句话说，一个句子是否可以使用间接问句，和动词、表语形容词或介词的语义有关。以下为常接间接问句的动词、表语形容词或介词的语义分类在；

1 询问类：ask, inquire, wonder, investigate;

2 知晓类：know, find out, remember, certain;

3 猜测类：guess, estimate, predict, judge;

4 告知类：tell, inform, point out, show;

5 决定类：decide, determine, make up one's mind, agree;

6 依赖类：depend, have a bearing, influence, affect;

7 重要类：significant, important, matter, care;

8 涉及类：concern, about, as to, regarding;

9 惊讶类：surprise, amaze, amazed, amazing; (限于特殊问句）

10 怀疑类：doubt, doubtful, question, questionable; （限于一般或选择问句）

当一个句子的谓语动词、表语形容词或介词为以上语义类别时，我们常可以后接间接问句。

上述第1、2、4、5、8类语义，常可后接疑问词+to do来表示间接问句。这种间接问句的答案带有祈使句的意味，而且常常以祈使句作为答案。因此此类问句也叫做祈使性问句。正因为祈使句是告知、要求、允许、同意某人做某事，因此祈使句的主语必须是人，即不定式的逻辑主语必须是人。这就是为什么疑问词+to do这个结构中不能用被动不定式。例如：

He asked how to pass the exam. I told him," Study harder."= I told him to study harder.

题外话：以上第6、7、9、10类语义的动词、形容词或介词不可后接疑问词+to do不定式。以下四句都是错误的，应该为适当的包含限定动词的宾语从句：

I doubt whether to accept.

It was amazing what to offer.

It depends on how much to pay.

I don't care whether to go or not.

以上系根据Huddleston《剑桥语法》有关内容整理。

继续补充

生成语法根据疑问句的答案，将疑问句在语义上分成信息性问句和祈使性问句。前者的答案为提供某个信息，是一种陈述；后者的答案通常为祈使句，而问句的目的就是征求听话人的建议、允许、批准等。绝大多数的问句是信息性问句，少部分问句是祈使性问句。例如：

信息性问句：

Did he read the book?  Yes, he read the book.

Did he arrive today or yesterday? He arrived yesterday.

When did he come back? He came back last week.

祈使性问句：

Shall I open the window? Open it./Go ahead.

Shall I revise it or rewrite it? Rewrite it.

When shall I come back? Come back before 9.

当这样的问句作为名词性从句时，它们仍然在语义上保持着信息性问句或祈使性问句的性质。

I asked him/I told him/It depended on where she was. = I asked him/I told him/It depends on the answer to the question "Where is she?"(信息性问句。）

祈使性问句则是说话人要求或给予建议、允许、批准等：

I told him what he should do. = I told him what to do.

He asked me how he can do it. = He asked me how to do it.

祈使性问句的特点是，从句谓语动作是未发生的动作，是建议、允许、批准在将来才做的动作。正是因为这种祈使句的意义，使得祈使性问句能够简略成疑问词+to do的形式。换句话说，只有祈使性问句才有两种间接问句形式：完整的限定动词问句形式和简略的疑问词+to do形式。也就是说，疑问词+to do 一定是祈使性问句。信息性问句不可以采用疑问词+to do的简略形式。也正因为祈使性问句的祈使意义，疑问词+to do不用被动形式。

I don't know where I am. 不能改写成 I don't know where to be.

I don't know what should be done. 不能改写成 I don't know what to be done.

what should be done的答案是this or that should be done. 即一个陈述，该问句是一个信息性问句，而不是暗示某人（句子主语或宾语）做某事的祈使性问句。按照Huddlestone的观点，信息性问句是没有疑问词+to do这种不定式问句形式的。

学习语法，是要掌握其原理、原则，以便能够推广应用，而不在于具体一个句子的正确与否。一个间接问句之所以能简略成疑问词+不定式，是因为这个是个祈使性问句，即问句中的主语和主句中名词一致，为祈使句的主语，因而可以省略主语；祈使性问句的动作是还没有发生的动作，故用不定式表示还没有发生的动作。于是省略主语和情态动词，得到疑问词+to do这样的简略不定式问句结构。明白这个道理，你就知道为什么疑问词+to be done是不正确的。即使偶尔有人使用，也是错误的使用了这个结构。因此，我建议网友将疑问词+to be done按照语法错误对待。自己写作英文时一定不要使用。

回复刘老师：

我认为：

可以说：I can't decide what should be done. 

不可以说：I can't decide what to be done.