The most common and most likely answer to this crossword clue is the 9 letter word SOCIOPATH
I've seen this crossword clue in Independent
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More clues leading to the result SOCIOPATH
Buddy explains!

The straight part
We know that "&lit-ish again – a sociopath might be involved in a shooting incident with a cop – whether shooting or being shot at?!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case &lit-ish again – a sociopath might be involved in a shooting incident with a cop – whether shooting or being shot at?! = sociopath.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 SOCIOPATH mean?
SOCIOPATH noun- A person with an antisocial personality disorder, exhibiting antisocial behavior that usually is the result of social and environmental factors in the person's early life.