I would say it's an adverb (faintly) that modifies an adjective (unreal), which then modifies a noun (quality). A faintly unreal quality. Adverbs can modify virtually everything, and so are often used to modify adjectives.
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Kooyeen.At least verbs, adjectives and other adverbs.
Adverbs can modify virtually everything, and so are often used to modify adjectives.