In a manner showing signs of fraying, tearing, or becoming worn and tattered at the edges.
From 'fray' meaning to unravel or wear away, plus '-ed' for adjective formation, plus '-ly' for adverb formation. The word builds systematically from the root verb through standard English morphology.
This is a wonderfully constructed word that shows how English lets you build complex adverbs from simple verbs—'fray' + 'ed' + 'ly' creates a single word capturing the whole visual idea of something coming apart in a tattered way.
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