Loss paid off in assignment (8)
I believe the answer is:
disposal
'assignment' is the definition.
(thesaurus)
'loss paid off' is the wordplay.
'off' indicates an anagram.
'loss'+'paid'='losspaid'
'losspaid' is an anagram of 'DISPOSAL'.
'in' acts as a link.
(Other definitions for disposal that I've seen before include "Scrapping" , "Riddance" , "Deployment - management" , "Out of control," , "Act of throwing something away" .)