Who would own the private police force? Only shareholders have standing to sue for securities fraud. The scenario you are describing is more like users of a product suing the provider. Users of a product can’t sue for securities fraud but can sue for breach of warranty of tortious conduct like negligence.

We don’t need to privatize the police force to be able to sue them for the harm they cause. Police already get sued a lot for their misconduct in civil court [1]. Civil cases are easier to win because the burden of proof is lower. The citizens (analogous to the shareholders) have just been unable (or unwilling) to hold them accountable for the harm they’ve been causing.

[1] https://www.chicagoreporter.com/chicago-spent-more-than-113-...