That's not correct. Liability is avoided now because of state governments mandating who is subject to what liability. Case in point, limited liability corporations and companies are legal fictions created by states. The business license one files to create a limited liability firm doesn't exist without the state government. Without that limited liability, your company - and you as the owner - are subject to much, much greater liability for damages.
As for how that should happen, I think secession would be the best method of achieving that sort of society. Providing saleable shares of public property to the next political subdivision down (for example, from the US federal government to the several States, each state to the counties within it, each county to the municipalities, etc.) would provide an avenue for restitution to victims of theft and abuse.
There are plenty who have tried it. Irwin Schiff died in in prison for trying to withdraw his consent to be taxed for things he didn't want the US government to do. As for not overthrowing the government, don't get me wrong: violence against so-called agents of the state is completely ethically justified. It just accomplishes nothing and makes things worse to an overwhelmingly greater degree than it helps. I'm all about using violence in self-defense and defense of others.