Here's such a sentence:
His dad needs to find what magazines he grew up reading.
The 'what' here is the object of the main clause.
His dad need to find what magazines (object).
The subordinate clause here is:
what magazines he grew up reading.
The subordinate clause without dangling modifier:
(what magazines) he grew up.
The dangling modifier:
reading (what) magazines.
So you see, 'what magazines' here is
- the object of the main clause,
- the object of a dangling modifier of the subordinate clause.
Is this sentence grammatically wrong? I've never seen sentences like this before. It sounds natural to me, though.
Notes: I didn't learn grammar in English, so some of the names may be misused.
For those who may ask, this sentence is inspired by a line of a recap. The original sentence is
I think his dad needs more time to know his son, understand his preferences, and maybe find what magazines he grew up reading.