The most common and most likely answer to this crossword clue is the 8 letter word WORDLESS
I've seen this crossword clue in Independent
W
O
R
D
L
E
S
S
More clues leading to the result WORDLESS
Buddy explains!

The straight part
We know that "staying silent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case staying silent = wordless.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 WORDLESS mean?
WORDLESS adjective- Conveyed without the use of words; unspoken or unsaid.
- Unable or unwilling to speak; dumb, silent or inarticulate.