Crossword Genius

Exhausted a debated possibility (4,4)

Ross

I believe the answer is:

dead beat

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

'a debated possibility' is the wordplay.
'possibility' indicates an anagram (another possible arrangement of the letters).
'a'+'debated'='adebated'
'adebated' with letters rearranged gives 'DEAD-BEAT'.

(Other definitions for dead beat that I've seen before include "wanting to retire?" , "Completely exhausted (colloq.)" , "Layabout" , "Informally a down-and-out" , "An American down-and-out" .)

I've seen this clue in The Globe and Mail.
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