Here's the short answer: contracts.
For the long answer: one of the keystones of libertarianism is the non-initiation of force. The other keystone that's relevant here is voluntary association through contracts. There are circumstances under which individuals should be considered incapable of participation in contracts. Here are a couple of scenarios:
- Children need limited exemption from contracts. For example, a 5-year old can be considered qualified to handle small amounts of money for buying items like candy, bread, etc. but not rat poison.[1]
- Everyone needs a limited exemption from contracts when they are drunk, drugged, groggy, etc. Otherwise, a robber may break into a self-drugged home-owner's house and ask for "permission" to take away some its contents. The owner house may "agree", but that can't be considered a voluntary association.[2]
With this in mind, let's look at the scenario you brought up:
- You get indebted to that corporation by your basic survival needs as you grow up
No, if such a situation arises, it's the parents who become indebted. The child can't be considered capable of consenting to major life decisions.
- The indebtedness - while "voluntarily" entered in by your parents giving birth to you there - can not feasibly be escaped.
The parents may even sign up for indentured servitude, but they can't sign their children into it.
Q. What about the situation where indebtedness can not feasibly be escaped, even if you yourself aren't in debt when reaching the age of consent
I have no literature for this, but judging by current events, when living in one country becomes insufferable for some people (as it is for some Mexicans, Cubans Burmese, etc.) people escape despite the risks of the journey. This works as long as there are relatively friendly destinations for the emigrants. So, for a teenager who is about to come of age, such an escape could be an attractive option.
There's another way out: many people in first-world countries have a strong preference for fair trade goods, even if such goods are sometimes more expensive than other options. This is a live demonstration that non-governmental agencies can do a lot to correct iniquities. Social movements have been quite effective in getting companies to be more eco-friendly. For example, Greenpeace (an agency that I agree with about half the time) has a large list of its successes. Some of those "success stories" involved making new governmental regulations, but others worked by just generating a lot of negative publicity for their targets. Naturally, the negative publicity let many customers to boycott certain companies. NGOs could play an analogous role in a laissez faire economy too, and get an ironhanded libertarian society to be more lenient.
I am not saying that these methods are fail-proof, and are guaranteed to fix all that ails a libertarian society. I am saying that these examples show that there are methods consistent with a free-market ideology that have been known to fix some such situations.
Footnotes:
The paper by John Hospers, Libertarianism and Legal Paternalism, touches on some of the aspects of exceptions to consent that I explained above.
[1] When the twelve-year-old is offered some L.S.D., with the invitation
"It'll give you a wonderful high," he may accept it eagerly, just as a baby
might play with a stick of dynamite or a loaded gun. For this reason, contrary
to what some libertarians apparently believe, all such invitations by
others should be prohibited by law, for the child's protection. The child
cannot give informed consent, much less "educated consentn-and those
who would take advantage of the child's incapacity should be met with the
full force of the criminal law. To say of the child that "after all he gave his
consent" would be ludicrous if its consequences were not so tragic.
And the following describes a more outlandish situation than what I described above, but the motivation in both cases remain the same: that there are situations when people should be considered incapable of giving consent.
[2] A person may be mentally deranged; but lacking this
extreme, he may be in a daze, or drugged, or in an acute state of grief or
depression, or just simply confused. Ordinarily when a person is in such a
state he can hardly be described as "fully informed," and so his action
would fail of voluntariness by the second criterion.