You keep using that word
So my first point is that sovereign does not mean what you think it means. Just because a state is sovereign, it doesn't mean that they are independent. There are several systems of government where smaller regions are sovereign but not indepent. Federations are nations that are formed by a Union of Soverign States that cede limited powers of government to a singular government body that speaks for all member states on matters of those powers. Examples of Federations include the United States of America , the Swiss Confederacy*, Canada, Australia, Germany (with the sub-regions being called States, Cantons, Provinces, States (again), and Bundesländer (aka Länder singular Bundeslander aka Land) respectively. A reverse situation also exists called a Devolution where unitary states cede partial soveriegn powers to regional government but retain some government powers. The United Kingdom uses this system where Parliment does grant Scotland and Northern Ireland limited regional government rights, while keeping those same powers for England and Wales. In either situation, the self-governing matters means that both a national government and a regional government are sovereign and may disagree on the areas of legal power it still retains and the citizens are under dual sovereignty (for example, if a man in New York state kills a man, he can be tried by both the State of New York and the Federal Government of the United States in theory... in practice, the Feds will defer to the outcome of the state trial as much as possible).
So are there nations that allow regions to leave?
No... but there is a term for this: Confederation/Confedercy (and no, the Swiss Confederacy is not a confederacy under this term... the title derrives from Confederacy and Federation being the same thing back when the Swiss cantons united). In a Confederate Government, a group of member states will create a single government to deal with certain matters, however the national Government has no real power over the State Governments. While no true confederated nation exists today, they did exist in history. The most famous, the Confederate States of America, lasted for five years from 1860-1865. Less famous was the United States under the Articles of Confederation from March 1, 1781 until March 4, 1789, when the United States Constitution was adopted to replace the Articles of Confederation. The big difference between Confederations and Federations (other than three letters) is that the Former exists when the United Government has equal or less power than the member states. The United States of America had very little national government power under the Articles and the ways in which it was an abysmal failure could be it's own response and while the CSA government basically copied the United States Constitution (the only changes is the Confederate President had a single six year term and a line item veto) by 1865, the CSA was facing it's own possible succession crisis as Texas, Georgia, and North Carolina each refused to send much needed troops and were considering leaving the Confederacy. A more succinct definition of a Confederation is that a Confederacy is a Federation where a state can leave if they are so inclined.
Given that is the fundamental difference, Confederacies work as provisional governments and short term polities while a stronger Federal framework is worked out. Use as a lasting government will usually ensure that the state does not last long (in the case of the CSA, the distrust of the central government by the states shares a large burden in it's failure to effectively manage the war.).
I do make the argument that the European Union is a modern confederation, however, it is a Super-National organization. If you want to accept that argument, than the EU nations cede only the power of Inter-State commerce and Movement to the "national government" and take all the other powers commonly ceded for themselves (such as foerign relations, international trade, immigration, and currency printing) with a slight oddity over the military (essentially using the United State's National Guard model for all levels of the military of the EU... that is, the E.U. member states have independent armies, navies, and air-forces that can be united under a single authority by the E.U. during emergencies but has no de facto standing military).