" "of my house" is a predicative or an attributive of "very little After the fire = temporal adjunct (time adverbial phrase) little = subject (noun) very = modifies the subject, an attributive adjective. After the fire ... remained of my house = predicate remained = verb of my house is a prep phrase, and an adjectival (modifies the subject = noun) predicative ( it is in the predicate) of the subject .
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