Crossword Genius

Fades away due to negligible expenditure in diet (4,3)

Ross

I believe the answer is:

dies out

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'negligible expenditure in diet' is the definition.
I can't judge whether this defines the answer.

'fades away' is the wordplay.
'fades' becomes 'dies' (I've seen this in another clue).
'away' becomes 'out' (similar in meaning).
'dies'+'out'='DIES OUT'

'due to' is the link.

Can you help me to learn more?

(Another definition for dies out that I've seen is " fails to survive".)

I've seen this clue in the Evening Standard.
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