As certainly anyone with a beating heart in their chest, there is nothing but disgust and anger towards the evil Ariel Castro who kept three girls for ten years in his basement after snatching them up off the street. Two of the three victims (Amanda Berry and Gina DeJesus) being returned to their families and justice will mete out to Castro, a scenario that even the most libertarian acolyte can admit still within the assumed role for government, but what of the third victim that had already been estranged from her family before being kidnapped? Libertarians not wanting the government to provide social workers to Michelle Knight, whom has no means to adjust after surviving such a tragic ordeal nor any support mechanisms since the her family (mother Barbara Knight was in an abusive relationship that endangered Michelle Knight's son) was the cause to her losing her child to the Child Welfare Services, would likely depend on charity to delivery such charity in a world with a negligible level of government service. In a high profile case such as Michelle Knight, there would be charities that would step up, but on the out of the spotlight tragedies such as Michelle's son being abused by Barbara's live-in boyfriend there is not enough charitable infrastructure to supply services to all of the victims of abuse on a daily basis.
In the Libertarian fantasy world, businesses unencumbered by any regulations and government interventions will rise and fall as new competitors creating market pressures on providing profitable services and products to the beck and call of consumers. Monopolies would be held at bay by individuals starting new firms all the time and magically having access to markets through hard work and gumption. But what is to be done to the victims of their circumstances, or victims of crime? Government would continue to dole out punishment to the perpetrators while the victims would just need to suck-it-up and get back to their job or start that Goliath succumbing start-up. Adjusting to life after suffer tragedy, someone out there could offer up for profit service, so that would be available if you could afford it, otherwise you would be out of luck. Who's responsibility for the injustices in the world, who is to make the effort to make things right? Only if you can afford to pay for justice and you consumer that is of a large enough market with dispensable income would you get assistance. Victims of violent crime, being an market that was serviced by a vibrant market of for-profit social workers would have an incentive to create more victims to continue their enterprise. World peace will never be provided when military contractors depend on continued war to profit; violence will always be with us as long as there is systemic incentives to continue servicing the aftermath of violence or selling implements of violence as products; poverty and starvation will end when it is no longer common place to privatize profits while socializing individual risk and liabilities on the least powerful of our society.
There is no market-driven solutions that prevents domestic abuse or child abuse, and dependency on charity to deliver such services when no social safety net is available is fraught with danger. Involuntary taxes paid to provide services, such as social workers to victims of their circumstances, regardless of the end user's ability to pay creates the possibility that a solution can be reached. A solution being reached is often the ideal for government solution (ex. a bridge is built), while a for-profit's ideal is never ending (ex. ferry service across a river); the ideal for the government is rarely met but it is better than the private market's ideal that is to turn the masses into Sisyphus eternally pushing the stone of profits up the hill every fiscal quarter. Though our social safety is the worse solution, it still is far better than all the other solutions.