Malfoy now turned to Hagrid.
“I’m not going in that forest, he said, and Harry was pleased to hear the note of panic in his voice.
“Yeh are if yeh want ter stay at Hogwarts,” said Hagrid fiercely. “Yeh’ve done wrong an’ now yeh’ve got ter pay fer it.”
“But this is servant stuff, it’s not for students to do. I thought we’d be copying lines or something, if my father knew I was
doing this, he’d ––“
(Harry Potter and the Sorcerer’s Stone)
There is a ‘for’ complementizer in the case. But when considering ‘do’ is a transitive verb, there needs to be ‘what’ or ‘that’. What grammatical explanations are there?
The for .. to construction here is misleading. The phrase is a marriage of two different constructions:
For here is not a complementizer, but an ordinary preposition:
It is [a job] for students.
And the infinitive is attributive:
They have [a job] to do.
That construction was discussed at this question. In the form I have just shown it is the direct ancestor of the modern semi-modal have to: “They have to do this job.
When you put these together you get “a job for students to do“, which looks like a defective nominal for .. to clause but is actually an adjectival prepositional phrase — serving here as a predicative complement.
Source : Link , Question Author : Listenever , Answer Author : StoneyB on hiatus