Undernourished family in Southern US city (6)
I believe the answer is:
skinny
'undernourished' is the definition.
(thesaurus)
'family in southern us city' is the wordplay.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'in' is an insertion indicator.
'southern' becomes 's' (abbreviation).
'us city' becomes 'ny' (I've seen this in other clues**).
's'+'ny'='sny'
'kin' going into 'sny' is 'SKINNY'.
(Other definitions for skinny that I've seen before include "little of substance?" , "Thin, bony" , "Not very well-built" , "not having much in the way of meat" , "Lean" .)