Disclaimer: If anything like this comes about lmaiseh, ask your LOR. Obviously, no practical advice should be taken from anybody on an online forum.
This is an issue which needs to be weighed heavily. Every tiny detail in every different scenario could be a huge game-changer. There are a couple of factors that need to be considered in every case – not just the specialized one NeutiquamErro posted (I’m not sure why he chose that case):
(i) The Abuser
(ii) The Abusers Family
(iii) The Victim
(iv) Potential Victims, aka Society.
(v) Yiddishkeit in General (Cheshbon of Chillul Hashem)
In the case you pointed out, there is little to gain by reporting to the government. There is no ????? ????? or ????? ????? (which would be involved in the Moser issue which we will discuss later), because there will be no more victims. The Abuser and his Family have only to lose – also something to go into later. The Victim gains nothing except ‘closure’, and Yiddishkeit would definitely suffer a great loss of Chillul Hashem, both among the Goyim and among ourselves.
I would say, therefore, that it would be both assur and wrong to report such a person. And absolutely no motive to do so besides revenge, which is not a Jewish trait. “Punishment” meted out by individuals is not something we have in Yiddishkeit.
What could possibly be a justifiable reason to ruin a family’s name? To make the wife and children walk through the streets with shame? To lose the abuser his job? To ruin generations of shidduchim? To ignite the fires of Loshon Hara and Sinas Chinam that already destroy Klal Yisroel?
There are other cases, however, which need more ????? ???? than this pretty clear cut situation.