Quicksilver was more or less right, but I’m still willing to take things from Lib’s point of view. So here goes.
Well. That does present a problem Libertarian. Let us say, hypothetically that a socialist government is set up in the United States. Private property, that which is considered the most important asset (or one of them) in libertarianism, would cease to exist. So where does that leave libertarians? at first glance, not in a very good position. But, in truth, for hard libertarians, the situation might be better than the one in the US now.
Let us take a theoretical situation. Socialist revolution in the US. The only violence from socialists was of defensive and retaliatory kinds. We have a government that is elected based on workers counsels, we start socializing industries.
We now have Libertarian and his family. You are employed by Large Widget Works. or LWW. LWW elects members to the citywide counsel, which in turn makes decisions on what LWW should do with employees and work output. If you do not like those decisions, even though they come from a democratic majority, you are free to quit LWW. You are also free to argue your case for Libertarian ideas, and attempt to become elected LWW representative to the city counsel.
Even though you have some success, and even win a few converts to the Libertarian view of life, most people are happy with socialism and what it brings them. They do not join with you. However, over the internet, you are able to find around 10,000 other people who share your Libertarian viewpoint. You petition the government. You and the other 10,000 people, feeling unwelcome and not fully being able to achieve happiness under socialism, wish to break off and form a libertarian subcountry. Now, depending on the strength of your proposal, and your skills in proposing it, this may or may not be accepted. There would be nothing under socialism to prevent it though. If it was not accepted you would be able to continue arguing for and submitting your proposal. Even form a political party to argue for it. As elections would be much more localized, it would be easier to form a viable party.
You could also quit your job and become self employed. Get approval from the local counsel, many of whom would know you and be more willing to listen than a state wide or national government, to form a little slice of libertaria right at home.
Now. Personal property, that which you have yourself, your home, your toothbrush, is still owned by you. It is still controlled by you.
But I fear that there will always be a definite split between socialism and libertarianism. Socialists wish to see the greatest possible good for the greatest possible number of people. This involves sometimes repressing the interests of the minority. But at least it’s done democratically. 