Confess -- keeping family, and going down (7)
I believe the answer is:
sinking
'going down' is the definition.
(sinking is a kind of going down)
'confess keeping family' is the wordplay.
'confess' becomes 'sing' (I've seen this before).
'keeping' is an insertion indicator.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'sing' placed around 'kin' is 'SINKING'.
'and' acts as a link.
(Other definitions for sinking that I've seen before include "Falling to the bottom" , "in decline" , "failing" , "Declining" , "Going down" .)