The most common and most likely answer to this crossword clue is the 6 letter word MUSLIN
I've seen this crossword clue in The Guardian
M
U
S
L
I
N
More clues leading to the result MUSLIN
Buddy explains!

The straight part
We know that "F/abric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case f/abric = muslin.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 MUSLIN mean?
MUSLIN noun- Any of several varieties of thin cotton cloth.
- Fabric made of cotton, flax (linen), hemp, or silk, finely or coarsely woven.
- Any of a wide variety of tightly-woven thin fabrics, especially those used for bedlinen.
- Woven cotton or linen fabrics, especially when used for items other than garments.
- A dressmaker's pattern made from inexpensive cloth for fitting.
- Any of several different moths, especially the muslin moth, Diaphora mendica.