There's been police and SS involvement with our neighbours - but still they get two very young kids left alone with them, despite some obviously overwhelming problems. My own kids have often had to listen to them calling their 3 and 5 year olds things you 'c!$t', 'little shit', 'retard' etc and have heard a few incidents that sound like someone being slammed against something, then a child cries. (And yes we called the SS/police/contacted the NSPCC).
Last summer, another neighbour overheard an incident where the 3 year old got burned when they were BBQing. And rather than rush the child to hospital, she says they were arguing loudly for ten minutes whose fault it was - the man trying to blame the woman and vice versa, presumably so they'd have the story straight at A & E. My neighbour thought, from what she heard, it was an accident but we did wonder if the kids might finally get taken into care after it (parents are permanently pissed/drugged up so even an 'accident' might point to negligence, esepcially with people with form). But no. The SS signed them off ages ago and no-one even seems to have been remotely suspicious even when the child was burned.
So in the context of an otherwise uneventful family with no prior form, no relationship with the coppers and the SS - I think the days of the SS charging in and running off with your kids are long gone. Seeing as they seem to leave actually abused kids in situ, now.
My worst one was when my 4th son stuck his toe into the piping hot tap when he was in the bath and got a nasty burn on his big toe. It happened right at the time his birth dad was dragging me through the courts for residency and trying to prove I was a crap parent and the kids ad a guardian ad litem, who was a social worker, as part of the court process. Totally nothing happened. Ex never got to hear of the accident, and everyone was perfectly satisfied I was an OK parent, and not neglectful just because my toddler had stupidly stuck his toe in a tap!