Put under joint ownership? A rejected suggestion (5)
I believe the answer is:
shred
'suggestion' is the definition.
(thesaurus)
'put under joint ownership? a rejected' is the wordplay.
'put under joint ownership?' becomes 'shared'.
'rejected' is a deletion indicator.
'shared' with 'a' taken away is 'SHRED'.
(Other definitions for shred that I've seen before include "Small part" , "Bit; cut or tear into tiny strips" , "(Reduce to) small piece(s)" , "Tatter; small amount" , "Dispose of" .)