The most common and most likely answer to this crossword clue is the 7 letter word PLACKET
I've seen this crossword clue in The Guardian
P
L
A
C
K
E
T
More clues leading to the result PLACKET
Buddy explains!

The straight part
We know that "piece of fabric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case piece of fabric = placket.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 PLACKET mean?
PLACKET noun- A slit or other opening in an item of clothing, to allow access to pockets or fastenings
- A petticoat, especially an underpetticoat.
- (by extension) A woman.
- A woman's pocket.
- A leather jacket strengthened with strips of steel.
- An additional plate of steel on the lower half of the breastplate or backplate.