The only proper, moral purpose of a government is to protect man's rights, which means: to protect him from physical violence--to protect his right to his own life, to his own liberty, to his own property and to the pursuit of his own happiness. Without property rights, no other rights are possible.
One is here tempted to wonder where property comes from, if it is to be synonymous with human life in our political values. Elsewhere, Rand's answer is similar to Locke's: "property," the concept by which materials cannot permissibly be taken from an individual to whom it "belongs," is created when said individual mixes his labor with it. Work, mentally and bodily, creates property from gross earth.
The trouble with this conceit is that it reeks of the mysticism she so defiantly claims to reject. Nothing in the laws of nature, to which Objectivism claims to owe its origins, corresponds to property. Life and death, troublesome concepts that they are, seem to exist objectively. The empirical evidence toward this conclusion is overwhelming. We can examine plants and animals in any number of ways and determine, physically, whether or not they are alive.
We cannot do this with property. No force field surrounds my car, protecting it from thieves. A physicist examining the car would not be able to determine any essential change in the car were I to sell it while she were examining it: she would not suddenly look up, a puzzled expression on her face, and mutter,"I sense a disturbance in the force...a document changing hands...insurance rates getting higher..." (In this example, the physicist in question is a Star Wars fan, and the car has been sold to a 17-year-old boy in another state.)
What protects the car from thieves--so far--is not a metaphysical fact but a social agreement to establish documentation of "ownership," and to maintain a persistent threat of violence toward those who would seek to challenge the authority of said document. The car ceases to be property when the community ceases to treat it as such. Under feudalism, we are entirely comfortable saying that property is created by soldiers, and you own what you are willing to expend resources to defend. Rand seems to believe that, faced with solidifying borders, technological improvements, mass production and international trade, humans suddenly discovered an a priori law of property that had always been there, written in the very eros of our being, and that it had no relation whatsoever to that earlier, fake "property" concept that had been developing and adapting to changing conditions since prehistory.
Rand treats property as a deontological law, as brutal and uncompromising as the God of Abraham. It must be followed because it must be followed. And because it must be followed, violence that preserves the law must be morally legitimate, whereas violence that threatens the law is forbidden. Rand prefers to express this concept in the form of a mugging--"A holdup man seeks to gain a value, wealth, by killing his victim; the victim does not grow richer by killing a holdup man."
In the interest of being needlessly pedantic and snarky, I would suggest that a "holdup man" is probably hoping to avoid killing his victim, which is why he goes to the trouble of the "holdup" instead of flat-out murdering a stranger and looting their corpse. I am also unclear on whether or not it is strictly correct to call the person who kills the holdup man a "victim," given that only one of them is still breathing. Rand does herself a rhetorical favor by putting this parable in a readily recognized situation, and one that takes place in a society several orders of magnitude more complex, and interdependent, than the noble savage groove she's been rocking so far. It also conceals any essential difference between a wallet held by clothing affixed to the body and a patch of land in another country, or the right to translateFinal Fantasy V into English at some point in the future. It also makes property-defending violence perpetually secondary, despite the fact that the laws of physics give equal claim on any object to anyone. "Objectively," the mugger's seizing of the wallet is no less moral than the "owner's" decision to carry it around in the first place. The distributed threat of violence to protect the social construct, in addition to providing the mugger with an incentive to leave his victim alive in the first place, is primary. The decision that any action is forbidden, and must be deterred with violence, precedes any violence the decision might forbid.
This distinction matters because elsewhere, Rand is keen to note that slavery is not a properly "human" state, and mere survival is not sufficient to rational living. On the contrary, nearly suicidal behaviors can be considered rational if the "life" one risks is one of servitude, terror, and uncertainty. It is difficult to argue with this point, and every moral system acknowledges that there are different kinds of life, and different kinds of death, and one need not act on akrasia to choose the final death of the rebel over the living death of the slave. Rand is in agreement with nearly everyone here. She just happens to have added the caveat that this does not apply to countries with strong property laws, in which case those unable to procure "rational," "independent," "human" survival by their own ingenuity and labor are morally obligated to suffer and die, intentionally remaining in lives of danger and want, even if they could improve their long-term chances of survival by seizing the property of another. They must die, so private property can live.