The most common and most likely answer to this crossword clue is the 7 letter word ASSUAGE
I've seen this crossword clue in Financial Times
A
S
S
U
A
G
E
More clues leading to the result ASSUAGE
- Calm a couple of sons united by length of life
- Calm a mathematician's mounting ecstasy
- Pacify ace German mathematician returning to base
- Soften cooked sausage
- Soften when wise man stores uranium
- Calm, outstanding union leader, equally wise
- Moderate embrace when yours truly leaves on time
- Call for lower pay for donkey work, say?
- Moderate university blocking unnamed WikiLeaks man
- Temper shown by idiot for all to see over period
Buddy explains!

The straight part
We know that "Soften" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case soften = assuage.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 ASSUAGE mean?
ASSUAGE 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.