For quite some time I've been noticing clauses of the type exemplified in this sentence: "Mr. McCain was asked what would Republicans do in response." (from the NY Times here). Traditional grammatical description often calls the bolded clause a noun clause, but following the CGEL, and for good reason, I'll call it a content clause.
The thing that's wonky about it, if you haven't noticed, is that interrogative content clauses don't typically undergo subject-auxiliary inversion. That is, you would expect Mr. McCain was asked what Republicans would do in response, with would following the subject instead of preceding it. I hear these on the radio all the time, but they're ephemeral, and I'm rarely positive that what I've heard is reported speech as opposed to a quotation or pseudo-quotation along the lines of Mr. McCain was asked, "what will Republicans do in response."
The example here, however, is unambiguous, and not just because of the punctuation. The use of backshifted would instead of will clearly signals reported speech rather than quotation.
There are only 46 examples in the COCA, at least using this search ([ask] + question word + modal + pronoun). And another 71 if you change the modal to be. You could do this with other auxiliaries, but obviously, it's unusual. Because of its rarity, it's difficult to look at the change in frequency over time, and indeed there's no pattern that I can see, but it is clearly most common in speech.
Another type of content clause that's doing weird things is the type following about as exemplified here: "I mean, every time you hear about we want a bailout, we need money, I get it." (You can get more examples here.)
I would expect either a non-finite clause (e.g., I mean, every time you hear about people wanting a bailout...) or an interrogative content clause (e.g., I mean, every time you hear about how people want a bailout...). But instead, we get a simple declarative content clause, in other words, one that is subordinate, but has the normal syntax of a typical main clause.
This type of wonky clause is more common than the first type, and the graph at COCA shows a trend towards more frequent use, though I don't know whether this is significant or not.
I wonder if there's any link between the two.