Long subjects in indirect questions

I know that to indirectly ask:

What is your name?

I should say something like:

I don't know what your name is.

But what if the subject of question is longer than "your name"? Something like:

What is the benefit of closing school when there's a flu outbreak

It just doesn't sound so good to me to indirectly ask the above question when the distance between what and is gets too long:

I don't know what the benefit of closing schools when there's a flu outbreak is.

So, I am wondering if it is Ok to ask the indirect question like this:

I don't know what is the benefit of closing schools when there's a flu outbreak.

I understand your dilemma, but putting is before the benefit is not a good idea. In an indirect question, there is no subject-verb inversion:

• Normal: you were here (subject, finite verb).

• Direct question: she asked: "where were you?" (finite verb, subject).

• Indirect question: she asked where you were (subject, finite verb).

In speech, you can't hear punctuation, and so only the tone at the end of the sentence (it goes up only in direct questions) and the word order differ.

There are also indirect questions embedded within direct questions:

• Did you ask her | where she was?

Here the tone goes up because the main clause is a direct question (hence the question mark); and so word order is the only difference between the two. As a result, some people are a bit sloppy with word order in indirect questions in writing and use inversion; but this is not recommended by style books, nor by most educated speakers. But you will see it occasionally, especially in longer sentences.

In your example I agree that putting is at the end makes the sentence unwieldy. The solution would be to move is more to the front, but not before the subject:

I don't know what the benefit is of closing schools when there's a flu outbreak.

Or:

I don't know what the benefit of closing schools is when there's a flu outbreak.

While I would not say your form is ungrammatical, I would say instead:

I don't know the benefit of closing schools when there's a flu outbreak.

To keep the "what" in play:

I don't know what the benefit of closing schools is when there's a flu outbreak.

or

I don't know what the benefit of closing schools might be when there's a flu outbreak.

Here's another idiomatic construction you might consider:

I don't know what benefit there is to closing schools when there's a flu outbreak.