Extraterritorial obligations of citizenship are the duties a state still imposes after you leave its territory: tax, reporting, military service, sanctions exposure, and in some cases criminal jurisdiction.
Most countries tax residents. Leave, break tax residence, and the claim on foreign income usually ends, subject to exit taxes and trailing-resident rules. A few states tax citizens. The United States taxes citizens on worldwide income wherever they live, a rule the Supreme Court upheld in Cook v. Tait in 1924. Eritrea does a version of the same. France has proposed citizenship-based rules for people who move to countries with substantially lower tax. The UK and the Netherlands have separately pushed exit taxes on people who leave. Residence-based systems are not always clean exits. Citizenship-based systems are not exits at all until you renounce.
Reporting is the daily version of the same problem. FBAR, FinCEN Form 114, is due when foreign accounts hit $10,000 in aggregate at any point in the year. It is not a tax form. You file it even if you owe nothing. FATCA Form 8938 attaches to the US return above higher thresholds. Foreign banks become reporting agents. A Plan B passport does not remove US-person status. The second document can even make the file look more complicated to a compliance team if tax residency is sloppy.
Military service is the other obligation that ignores where you grew up. South Korea requires men to serve 18 to 21 months. Male dual nationals must choose a nationality by 31 March of the year they turn 18. Miss that window and you generally cannot renounce Korean citizenship until you serve or age out in your late thirties. Israel conscripts citizens, including many who also hold another passport. Singapore locks male citizens and some second-generation PRs into national service. Greece can stop men with Greek nationality from leaving until service or a formal deferment is settled. Russia conscripts dual nationals on Russian soil and treats the foreign passport as irrelevant there. Switzerland drafts men who live in the country; citizens resident abroad are generally exempt in peacetime if they have deregistered, and they become liable again if they move back. Sanctions and capital controls travel with the passport number. When a state is sanctioned, its nationals inherit bank de-risking they did not personally earn. When a state imposes exit taxes, wealth taxes, or currency controls, citizenship or lingering residence can keep you inside the net. Criminal jurisdiction can follow too. Some states claim the right to prosecute nationals for acts committed abroad.
This is why a passport is a legal relationship, not a souvenir. Before you add a nationality to the portfolio, map what comes with it. Annual filings. Draft rules and the age windows. Whether the country allows you to hold another citizenship. How hard it is to renounce, and whether you can renounce at all before service. A Plan B that creates a permanent tax or service obligation is not a Plan B. It is a new concentration. The inventory belongs next to the application, not after issuance.
Related: accidental citizenship, Plan B passport, wealth migration.