Do we need to explicitly mention the antecedent in an attributive clause inside another one, both describing the same antecedent?

A sudden question popped up in my head just now: which of these two sentences are correct, or are they both wrong?

  1. I write books that nobody reads or even knows that they exist.
  2. I write books that nobody reads or even knows that exist.

I think what I am trying to express with these sentences should be pretty clear: that this person writes books, but their books do not sell, and moreover no one even knows about these books' existence.


Solution 1:

In each of those two examples, the second subsidiary clause is ungrammatical, even without the first subsidiary clause. In your sentence 1., one problem is the explicit "they" -- this should not be explicit. In your sentence 2., the problem is "that exist". This would be ungrammatical even if reduced to

2.b. I write books that nobody knows that exist.

However, this is OK:

3.b. I write books that nobody knows exist.

so, returning to your earlier examples:

3.a. I write books that nobody reads or even knows exist.