The most common and most likely answer to this crossword clue is the 9 letter word CAMELHAIR
I've seen this crossword clue in Financial Times
C
A
M
E
L
H
A
I
R
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 = camelhair.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 CAMELHAIR mean?
CAMELHAIR noun- The soft hair of a camel.
- A substitute for this hair.
- A soft fabric made from this hair.