Smallest amount went stale (5)
I believe the answer is:
least
'smallest amount' is the definition.
(I've seen this before)
'went stale' is the wordplay.
'went' indicates an anagram ('go' can mean move).
'stale' with letters rearranged gives 'LEAST'.
(Other definitions for least that I've seen before include "Bottom" , "Smallest (in significance)" , "Lowest or smallest" , "Lowest amount" , "Of minimal significance" .)