noun of noun (relative modifier)

Hi Kilimanjaro

Two things are common to your sentences: both contain a restrictive relative clause and an of-genitive. As a door normally has only one handle and a house has only one roof, the relative pronouns can't refer to handle and roof. For that to be possible, the sentences should read:

He seized the handle of the door, which was broken.
The roof of the house, which has long been dilapidated, needs an overall restoration.

These sentences are truly ambiguous. It is of course possible that the person who wrote the original sentences didn't intend the antecedents to be door and house but since there is no context, that is the only interpretation.

Cheers
CB