Relics moved man to break into tears (8)
I believe the answer is:
remnants
'relics' is the definition.
(relic can mean a remnant of something)
'moved man to break into tears' is the wordplay.
'moved' indicates an anagram.
'to break into' is an insertion indicator (inserted letters break into the word).
'tears' becomes 'rents' ('rent' can be a synonym of 'tear').
'man' anagrammed gives 'mna'.
'mna' inserted inside 'rents' is 'REMNANTS'.
(Other definitions for remnants that I've seen before include "Stern man has left-over pieces" , "Bits left over" , "Remains" , "Pieces of fabric left over" , "Leftovers, scraps" .)