This is my Bachelor's Thesis in Linguistics on the syntactic and semantic identity conditions on sluicing.
In English, we're allowed to say things like "Someone is going to the conference, but I don't know who"; it's basically implicitly understood that "who" stands in for "who is going to the conference". It seems like an obvious fact, but consider the following example: "We're donating our car, but we don't know who[m]." That doesn't sound nearly as good. I could say "We're donating our car but we don't know to who[m]," and you would immediately get what I was saying. Why is this? Why does eliminating one tiny preposition lead to such a difference in how the sentence sounds?
Constructions like this, where a question word kind of "stands in" for a whole phrase, are called "sluices". Here I spend 8000 words discussing the things that make such sentences sound fine, and what happens when they sound bad. Some of the topics I cover are: the role played by morphological case in German and Icelandic and the question of whether the meaning of the pronounced clause needs to exactly match the meaning of the unpronounced one.
I am by far not the first person to discuss this phenomenon. In fact, in April 2019 I was lucky enough to be able to sit in on a whole conference about sluicing with some of the most interesting thinkers in the field.