Destroyed by the vice around Los Angeles (5)
I believe the answer is:
slain
'destroyed' is the definition.
(I've seen this in another clue)
'vice around los angeles' is the wordplay.
'vice' becomes 'sin'.
'around' indicates putting letters inside.
'los angeles' becomes 'LA' (abbreviation).
'sin' enclosing 'la' is 'SLAIN'.
'by the' is the link.
(Other definitions for slain that I've seen before include "Put to the sword" , "Killed, murdered" , "Violently killed" , "Slaughtered" .)