I don't think there's any one answer that all will accept on this question, but to simplify the sorting process for you, the real question you are asking is: "What is a state?" and then within this specifically the question of how such a state relates to its members.
In terms of philosophical theories of the state (in this case the polis), the earliest two philosophers, I know of, in the West who consider this question are Plato and Aristotle.
For Plato, the state is either a small village (early in the Republic) or a complicated system where the members of the state are split among three roles: philosopher-kings, guardians, and producers (for an extended treatment see here: http://plato.stanford.edu/entries/plato-ethics-politics/). On such an account, the parties all agree that this is the best way to accomplish justice as they are enlightened by its presence. On such an account, it makes no sense to split off from the state.
From what I understand, there's a different account in the Laws of how things should be arranged but I'm not familiar with the details.
Moving to Aristotle, Aristotle believed the state was prior to the individual and the family. What this means is that the state is the organic whole of human living (like a hive to bees or pack to dogs). On such an account, it seems unlikely that it would make sense to split off, but it seems distantly conceivable.
Many contemporary Aristotelians are communitarians which means that they think each community is determined by a shared set of values, and that these sets of values are incommensurate with others. On such an account, each community is a polis which can be held together in a larger federation -- but this federation is dissolvable.
Augustine in the City of God adapts elements of Plato's philosophy to present the idea of dual citizenship for Christians in Rome and Heaven. On such an account, the state below is more arbitrary and maleable since the image of justice is through religion not the state.
I'm not familiar enough with Aquinas's account of the state to provide the contours, but I gather it's a somewhat communitarian picture but not overly prone to allowing schisms emphasizing the holistic aspects of the Aristotelian picture.
Moving forward to Hobbes and Locke, we arrive at the idea that the state arises through negotiations of power and the surrendering of the right to bash others in (social contract theory). On such theories, I don't see the ultimate objection to schisms in the state. For instance, it's hard to see why such a contract isn't malleable enough to allow for that as say per se Scotland devolving or something like that.
In this era, we also see the rise of the consideration of notions of sovereignty. For Hobbes, sovereignty occurs either when people contract together and agree to follow a common authority or when people bandy together for mutual protection. This sovereignty is revokable --as makes sense under a contract theory of governance. As ben rudgers suggests, one clear method of revocation is to kill the sovereign. But it's less clear whether a sovereign can allow for secession on the part of some parts of the state. (Source for this paragraph: http://plato.stanford.edu/entries/hobbes-moral/)
For Locke, the contract works in such a way that most freedoms are granted to the citizens by the sovereign, but these are established in nature and self-evident. Thus, insofar as the state is legitimate, there should be no need to schism. Insofar as the state is illegitimate, schism is no longer the right word.
The Kantian picture of the state is a Republic guided by reason with the power of the state. Such an image depends on a type of federating where the size of the particular state is less important than the unity of the rational whole of humanity.
Hegel is similar to Kant in seeing the state as ultimately a product of reason and similar to Aristotle in seeing the state as an organic whole larger and prior to the individual humans and families that make it up. At the same time, the Hegelian picture depends on internal conflicts and their modifications. The net result of that is that Hegel would find such dissolution where states break apart to be a temporary resolution until their inevitable reunion in something larger and more complete as an integration between the individuals, families, the community, and Absolute spirit. (long story ...).
There's going to be some other theories to consider as well I'm guessing, but these are the ones I can sketch briefly.