On the first issue, of “freeloaders of government,” the second thread SN linked to is long, but near the end it strikes at the heart of your question and features good posts from different perspectives. In brief, it appears Ayn Rand was asserting that government should maintain a link between payment received and services rendered in civil matters, and general access to the criminal justice system. If one did not pay for the government, one would not have recourse to the civil court system, one would be free to make contracts for example, but one’s contracts go unprotected by government unless insured by payment of government services. Essentially, services follow from support, except in criminal justice.
Other Objectivists such as Leonard Peikoff and Yaron Brook uphold that irrational noncontributors or freeloaders can just be boycotted or ostracized by the otherwise rational people who recognize the importance of the government’s functions.
On the matter of having one’s property surrounded by someone else’s property, there are several usual responses, to this phenomenon called “encirclement.” First, it is pertinent to point out that under the status quo (statist quo?) that is the exact reason, historically, (and despite the usual reasons provided to the contrary) that government has monopolized roads and highways in the first place: to surround our property with easy access for the government’s agents, viz. tax collectors. Technically, we can’t go anywhere without paying for it already, whether we want to or not, since these public thoroughfares are funded by taxes.
Which brings us to the second point, that in a totally private property society, the fact still remains that our property will always generally be surrounded by other private property. Perhaps not in the way you are thinking, as in a person literally cannot get off his land to go anywhere, but nonetheless the fact still remains that in this hypothetical private property society, every point in the country is privately owned by one or another individual person in such a way that every owner of a piece of the surface of the United States finds that his property is surrounded by the properties of other persons.
Now as to the meat of your question, let us suppose that someone is literally surrounded in such close quarters by one piece of property, such that it is like a small island. And let us further suppose that those individual(s) that own the property surrounding his are his personal enemies or otherwise particularly mean and spiteful people. Our poor victim is trapped literally under imposed isolation.
As in any conflict, we must ask, how did this situation come about? One conceivable answer would be that the access way was previously public property which was “privatized” into the hands of our villains, who then proceeded with their vendetta against the poor trapped man. An obvious solution then would be that we must make sure to guarantee a stake in ownership and access to adjacent public roads during the transition program, so as not to create any such situation.
Which brings us to the next point, that whenever a property changes hands, we have a “title search” to determine the relevant facts about the property, namely what kind of restrictions or allowance pertain to the use of the land, so therefore we would have an “access search” in regards to road usage to ensure access and egress.
Another thing, is that this cannot happen on any sort of wide scale, as it would be in the financial interest of road owners to attract customers, so usually this kind of objection belongs in the category of those kinds of objections that go much like: “What if private road owners never allowed anyone to use the roads and we all couldn’t go anywhere?! Or, what if private road owners allowed destruction derbies on their roads and we all wrecked all the time?! Or, what if private road owners charged a million dollars to leave your house, we all would be stuck!” etc. For these objections we can only point to the fact that on the market such behavior would be nonexistent because prices are not arbitrary and such activities would have so high an opportunity cost as to render it impossible, especially for any profit-maximizing individual.
But let us proceed to your actual hypothetical. Suppose there is no such wild scheme at hand, and these are simply mean people who block a man’s exit forth from his property (or a man might refuse to pay the price they set, or what have you) in a single isolated case. (Or perhaps he is one of the freeloaders who refuses to fund government and the people are boycotting him, or some such thing?) In this type of case, it may well be that they are entirely within their rights. Denying someone use of your property is not an initiation of force onto them, not an invasion of their property. Secondly, this does not constitute actual imprisonment because you do not have three dimensional control over the person, there are any number of ways he can get out, just not over the adjacent land. Actual hostile encirclement cannot be any kind of widespread practice any more than torturing animals or espousing disgusting and perverted behavior or being a mean personal in general or what have you because those who engage in it can simply be counter-boycotted or otherwise ignored by other people who judge their actions to be unjust.
Civil law already takes a similar approach:
“Art. 693. Enclosed estate; voluntary act.
If an estate becomes enclosed as a result of a voluntary act or omission of its owner, the neighbors are not bound to furnish a passage to him or his successors.”
If all else fails, the individual can of course take his situation to a court of law and proceed to make his best argument for an easement or of some circumstance whereby the mean people have unjustly delimited his control over his own actual property by some fraudulent or indirectly invasive means. People would certainly be sure to guarantee access in contractual agreement when engaging in any kind of business regarding property relationships, therefore suing for fraud or breach of contract would always be an option in that kind of instance.
To wrap this post up, we must make clear that owning property rights in handcuffs does not grant you the right to go around and place them on someone else’s hands at whim or arbitrarily. In short, in most cases, the isolated owner has already homesteaded access and egress to his property during the time that the government owned the public roads or otherwise and hostile encirclement of him would be a violation of his rights. The problem of enclosing others’ property is not a new one only recently realized with Ayn Rand’s political philosophy, but have been around as long as private property has been around and the law has found ways to deal with it objectively.