The most common and most likely answer to this crossword clue is the 15 letter word TERROR-STRICKEN
I've seen this crossword clue in Financial Times
T
E
R
R
O
R
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S
T
R
I
C
K
E
N
More clues leading to the result TERROR-STRICKEN
Buddy explains!
The straight part
We know that "scared stiff" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case scared stiff = terror-stricken.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 TERROR-STRICKEN mean?
TERROR-STRICKEN adjective- Stricken with terror; utterly terrified.