End fell in fire - very negligent (5)

I believe the answer is:

slack

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'negligent' is the definition.
(similar in meaning)

'end fell in fire very' is the wordplay.
'end' indicates one should take the final letters.
'in' is an insertion indicator.
'fire very' becomes 'sack' (dismiss someone from their job. I am not sure about the 'very' bit.).
The final letter of 'fell' is 'l'.
'l' placed within 'sack' is 'SLACK'.

Can you help me to learn more?

(Other definitions for slack that I've seen before include "Not taut" , "Flaccid" , "Limp - negligent" , "Lax" , "Idle and disinclined to work" .)

I've seen this clue in the Sydney Morning Herald.

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