If a serial killer tried to break in your house, right now, how would police stop it? They wouldn't, they don't. They show up AFTER the damage is done. Police are nothing more than first responders, & extortionists of the fruits of other people's labor.
Why would you ever condone such immorality? They do NOT prevent crime. The greater concern should be the prevention of crime. The best crime prevention is a strong community. Solidarity with one's neighbors provides an increase in security and safety for all. The Amish and the historical record of the Native Americans illustrate how culture and community make a really big difference.
To fill this role of first responder, the people of the community would need to take steps to train everyone to act as a first responder able to deal with a wide variety of circumstances from car crashes to heart attacks.
This training would also need to address how authority can be asserted, and people can be organized in the event of an emergency. This is nearly identical to how a milita would form in a community to protect itself from an external threat.
There ARE already private EMS's, ambulances, etc. that is, groups which do some of those things and are not a "public" or state service (and so then obviously would not be effected in a negative way by the state being gone).
In fact, any of the things an individual imagines "government" to be responsible for, are only due to the actions of the individuals who engaged in those activities because they would be getting a pay check. All of the "services 'provided'" by the "government" can be provided by any group of individuals (other than enslaving everyone, the main 'government' program, anyway).
Living in accordance with Natural Law is the ultimate protection. Fully embracing your own personal responsibility, is the strongest and best crime prevention you can possibly have. Because the potential hardship that threatens any criminal likely to try you, then exists immediately whenever they try and do so, and in such a society, criminals would know this.
It's not rocket science that the guy with a badge & a gun, running radar for speeding tickets 3 miles away, who has a monopoly on force & violence, to protect you from criminals, is going to be virtually meaningless to any actual attempts made towards you by criminals.