The most common and most likely answer to this crossword clue is the 9 letter word ASSUAGING
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More clues leading to the result ASSUAGING
Buddy explains!

The straight part
We know that "Softening" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case softening = assuaging.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 ASSUAGING mean?
ASSUAGING verb- To lessen the intensity of, to mitigate or relieve (hunger, emotion, pain etc.).
- To pacify or soothe (someone).
- To calm down, become less violent (of passion, hunger etc.); to subside, to abate.
- The act of one who assuages.