Impecunious family in outskirts of Southport (5)
I believe the answer is:
skint
'impecunious' is the definition.
(I've seen this before)
'family in outskirts of southport' is the wordplay.
'family' becomes 'kin' (synonyms).
'in' indicates putting letters inside.
'outskirts of' means to remove the middle letters (only letters on the outskirts).
'southport' with its middle removed is 'st'.
'kin' placed within 'st' is 'SKINT'.
(Other definitions for skint that I've seen before include "Without money (slang)" , "Hard-up" , "Having little money" , "Stony broke" , "Strapped for cash" .)