Undernourished family in southern US state (6)
I believe the answer is:
skinny
'undernourished' is the definition.
(thesaurus)
'family in southern us state' is the wordplay.
'family' becomes 'kin' (synonyms).
'in' indicates putting letters inside.
'southern' becomes 's' (abbreviation).
'us state' becomes 'NY' (abbreviation for New York).
's'+'ny'='sny'
'kin' put within 'sny' is 'SKINNY'.
(Other definitions for skinny that I've seen before include "Euphemism for a caffe latte with skimmed (non-fat) milk" , "Very slim" , "Tight-fitting" , "Emaciated" , "far from stout!" .)