Imagine a world in which earth has started to colonize other worlds slowly, though the expense to send ships to other worlds is extremely high, and without FTL drive it takes some times to create a self sustaining colony. To support the building of these colonies governments have looked to the support of investors for financial backing. These backers are putting a significant expense into supporting colonization, both due to the high original colony ship construction expense and the opportunity cost of tying so much capital into a potentially risk effort, and will expect the colonies to make a pretty hefty repayment to cover these expenses. Effectively each colony is going to start out in significant debt and is going to be expected to work to repay their original colonization expense & interest over decades, if not generations, once they become self sufficient.
Due to the expense of of travel between worlds shipping supplies between worlds is almost never cost effective, thus a colony can not repay its debt by sending supplies back to Earth. However, the existence of reliable and high-bandwidth FTL comms has made an information economy viable, see second half of my answer here (Interplanetary commerce: how do you compare currencies?).
Colonies are small compared to earth, and don't tend to produce a significant amount of science or cultural resources, such as movies. However, many other forms of information exchange & economy exist. For instance, programmers on a colony may be hired to write software for a program being created on Earth, or telemarketers on a colony may call people on Earth to ask if they want to buy some product, or Amazon may by cloud computing power from servers built on the colony. A therapist or accountant or Engineer on the colony may tele-communicate with clients on Earth etc etc. Thus there are many ways to produce value for earth from a colony via ansible alone, which could be used to eventually repay investors. Likewise all the same serves can be purchased by people on the colony from earth, plus Earth having a much larger culture will have numerous works of media and science etc that the colony is going to want. Thus the colony is incentivized to do work for Earth to earn the money required to purchase the information/media it desires from Earth.
So in theory this sort of investment is viable to support colonization. However, the people on the colony will likely get frustrated with having much of their earnings from earth being taken to pay for interest on the original colonization fees incurred by their grandparents. Due to the high interest rate on colonization backed stocks and the decades, or longer, that interest had to build up before the colony was self sufficient and capable of starting to produce value to repay Earth the final colonial debt is high and will take a very long to repay. It would be tempting for the colony to write off its own debt and refuse to repay it rather then spend so long doing so, and Earth is too far away to send anyone to physically take back any of the supplies they sent to support the colony.
Thus the only means of enforcing repayment of debt is via market forces & restricting the colonies access to information from Earth until debts are replayed. The problem being that other colonies exist, any data that Earth sells to colony A can then be sold from A to B to C etc. In much the same way that another countries exports are often easy to pirate online because your home countries laws provide little protection/restriction from pirating media not produced within that country. If Earth-originated information were to start being 'pirated' earth would lose most of its means of compelling a colony to repay its own debts. Again, Earth has no way of imposing its laws about not pirating data on external colonies by force.
So, can Earth reliable gaurentee a means of enforcing a colonies will repay their debt, over whatever length of time it takes, once the colonies becomes self sufficient? Will economic forces be able to ensure this occurs? Or will colonies all revolt against their collective debt?
For now assume that Earth's economy is mostly integrated and consistent rules are enforced across all Earth Ansibe communications, regardless of country of origin. Ie, ignore inconsistency in laws and assume whatever laws Earth passes in regards to Ansible and colony debt are aided by. Also assume these laws are written to support the backers of colony ships by ensuring they will get repaid.
Also for now assume that it is possible, eventually, for colony to repay their own debt. I'm not sure this is true, it could reach the point where the interest on the debt grows faster then the colony can produce income to pay off the debt; but that will be a follow up question only after this one is answered.