I would again emplore you to read the book or at least the chapter I have linked earlier. All of these most common questions are answered.

I will post here the relevant section discussing this point:

"“But how could a poor person afford private protection he would have to pay for instead of getting free protection, as he does now?” There are several answers to this question, one of the most common criticisms of the idea of totally private police protection. One is: that this problem of course applies to any commodity or service in the libertarian society, not just the police. But isn’t protection necessary? Perhaps, but then so is food of many different kinds, clothing, shelter, etc. Surely these are at least as vital if not more so than police protection, and yet almost nobody says that therefore the government must nationalize food, clothing, shelter, etc., and supply these free as a compulsory monopoly. Very poor people would be supplied, in general, by private charity, as we saw in our chapter on welfare. Furthermore, in the specific case of police there would undoubtedly be ways of voluntarily supplying free police protection to the indigent — either by the police companies themselves for goodwill (as hospitals and doctors do now) or by special “police aid” societies that would do work similar to “legal aid” societies [p. 220] today. (Legal aid societies voluntarily supply free legal counsel to the indigent in trouble with the authorities.)

There are important supplementary considerations. As we have seen, police service is not “free”; it is paid for by the taxpayer, and the taxpayer is very often the poor person himself. He may very well be paying more in taxes for police now than he would in fees to private, and far more efficient, police companies. Furthermore, the police companies would be tapping a mass market; with the economies of such a large-scale market, police protection would undoubtedly be much cheaper. No police company would wish to price itself out of a large chunk of its market, and the cost of protection would be no more prohibitively expensive than, say, the cost of insurance today. (In fact, it would tend to be much cheaper than current insurance, because the insurance industry today is heavily regulated by government to keep out low-cost competition.)"