The most common and most likely answer to this crossword clue is the 7 letter word CHIFFON
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More clues leading to the result CHIFFON
Buddy explains!

The straight part
We know that "fabric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fabric = chiffon.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CHIFFON mean?
CHIFFON noun- A sheer silk or rayon fabric.
- Any purely ornamental accessory on a woman's dress, such as a bunch of ribbon, lace, etc.