- ...people who I have no idea who are.
- ...people who I have no idea who they are.
This is an example of a violation of what is sometimes called an ISLAND CONSTRAINT.
Often, a wh- word at the beginning of a relative clause or question can refer to an entity belonging to a clause much further away in the sentence structure:
- Who(i) did [Bob say [that Mary knew [that John had kissed ____(i) ]]] ?
- I know the girl who(i) [Bob said [Mary knew [that John had kissed ____(i) ]]].
However, there are some types of environment where we cannot have an antecedent gap for an earlier wh- word (another way of thinking about this is that you cannot extract a wh- word from this environment). These restrictions are commonly known as island constraints after a famous thesis by Ross (1967).
The Original Poster's examples in particular violate a wh- island constraint. This is some of what the Encyclopedia of Language and Linguistics has to say about wh island constraints:
Another such island constraint is the wh island constraint, which rules out extractions from wh clauses (clauses introduced by wh elements). Extraction from nonfinite wh clauses (as in Examples (11a) and (11b)) is not totally unacceptable, but extraction from finite wh clauses (as in Examples (12a) and (12b)) is much worse:
(11a)The librarian wondered [whether to put that book on the shelf].
(11b)?Which book did the librarian wonder [whether to put ____ on the shelf]?
(12a)I wondered [whether the librarian put that book on the shelf].
(12b)*Which book did you wonder [whether the librarian put ____ on the shelf]?
Notice that in English relative clauses, there must normally be a gap in the relative clause where we would expect the item represented by the wh- word to be. If speakers embark upon an illicit wh movement like this, they will often try to repair it by sticking a resumptive pronoun in where we expect the gap to be. So someone embarking upon (12b) might try to repair it as they went along like this:
12c *Which book did you wonder [whether the librarian put it on the shelf]?
(12b) is the equivalent of the Original Poster's example (1). The Original Poster's second example is a type of repaired sentence as in (12c). Neither would be considered perfectly grammatical by most speakers of standard Englishes.
The only way to make the Original Poster's examples grammatical is to rephrase them entirely.