Prostrate having done in backbone ... (6)
I believe the answer is:
supine
'prostrate' is the definition.
(thesaurus)
'done in backbone' is the wordplay.
'done' becomes 'u'.
'in' means one lot of letters goes inside another.
'backbone' becomes 'spine' ('spine' can be a synonym of 'backbone').
'u' placed inside 'spine' is 'SUPINE'.
'having' is the link.
(Other definitions for supine that I've seen before include "Lying face upward" , "Unresisting" , "offering no resistance" , "Inert; on one's back" , "Lying face upwards, indolent" .)