The most common and most likely answer to this crossword clue is the 6 letter word FAILLE
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More clues leading to the result FAILLE
Buddy explains!

The straight part
We know that "soft material" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case soft material = faille.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 FAILLE mean?
FAILLE noun- A fabric woven from silk, cotton, or rayon with slight ribs.