Survive having bad back (4)
I believe the answer is:
live
'survive' is the definition.
('live' can be a synonym of 'survive')
'bad back' is the wordplay.
'bad' becomes 'evil' ('evil' is associated in meaning with 'bad').
'back' is a reversal indicator.
'evil' backwards is 'LIVE'.
'having' is the link.
(Other definitions for live that I've seen before include "Being performed at the time of hearing or viewing" , "Possibly shocking" , "Present in person, not recorded" , "shocking potentially?" , "Exist in evil" .)