The whole structure "nowhere to be found" is an idiom that functions as an adverbial phrase of location. Grammatically, it's not that different from saying the ring was "here", "there", "on her finger", "in the jewelry box", etc. "To be found" is the passive infinitive of "to find." Within this idiom, it functions as an adverbial phrase within another adverbial phrase, since it further defines the adverb "nowhere."