Happy with coral being destroyed without proper backing (10)
I believe the answer is:
apocryphal
'without proper backing' is the definition.
'happy with coral being destroyed' is the wordplay.
'with' says to put letters next to each other.
'being destroyed' indicates anagramming the letters.
'happy' after 'coral' is 'coralhappy'.
'coralhappy' anagrammed gives 'APOCRYPHAL'.
(Other definitions for apocryphal that I've seen before include "probably made-up" , "Fabulous" .)