Crossword Genius

Dropped off where sleepers are grabbing a rest at last (6)

Ross

I believe the answer is:

abated

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'dropped off' is the definition.
(I've seen this before)

'sleepers are grabbing a rest at last' is the wordplay.
'sleepers are' becomes 'abed' (I can't justify this - if you can you should give a lot more credence to this answer).
'grabbing' is an insertion indicator.
'at last' says to take the final letters.
The last letter of 'rest' is 't'.
'a'+'t'='at'
'abed' going around 'at' is 'ABATED'.

'where' acts as a link.

Can you help me to learn more?

(Other definitions for abated that I've seen before include "grew smaller" , "Eased" , "Went down or became less, like storm" , "Calmed like storm" , "Became less strong or severe" .)

I've seen this clue in The Telegraph.
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