Sell the day's production endlessly (11)

I believe the answer is:

deathlessly

I'm a little stuck... Click here to teach me more about this clue!

'endlessly' is the definition.
Both the answer and definition are adverbs.
Maybe there's a link between them I don't understand?

'sell the day's production' is the wordplay.
'production' indicates anagramming the letters.
'sell'+'the'+'days'='sellthedays'
'sellthedays' is an anagram of 'DEATHLESSLY'.

Can you help me to learn more?

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

Want a hint initially instead of a full solution? Install my app