Can you travel when you're in "passport limbo"?
Depending on the country, sometimes the Japanese naturalization procedures require you to renounce your former citizenship(s) after acquiring Japanese citizenship -- within two years. This is for countries like New Zealand and the United States. However, For most countries, such as South Korea, the United Kingdom, and the People's Republic of China, Japan requires you to renounce/legally abandon your former nationalities prior to receiving Japanese naturalization.
Note that they won't ask you to do this until they've confirmed that every other detail of your application process will pass the requirements, so there's no risk of you renouncing your citizenship and then finding out that you won't be receiving Japanese citizenship. Even so, some countries have a "safety boomerang" clause for their renunciation procedure. For example, if citizens of the United Kingdom renounce their citizenship but do not manage to acquire another citizenship within six months, their U.K. citizenship is automatically restored.
For the case of nationals from the PRC (People's Republic of China), the Chinese Embassy will issue you a special travel letter document that will allow you to travel to Greater China (meaning not Taiwan, Hong Kong, or Macao) during the period where you've renounced your Chinese citizenship and cancelled your CN passport but you have not received your Japanese citizenship and passport yet. This document will not allow you to travel to any other country.
For Americans, there is a time when you apply for relinquishment of your U.S. citizenship and you send your U.S. passport to the State Department for processing. However, as you as still technically a U.S. citizen until the U.S. State Department has issued you a CLN (Certificate of Loss of Nationality), you are issued a letter from the embassy explaining that you are in the process and your U.S. passport is in possession of the State Department. This letter is solely for travel to the United States, and America requires those who are U.S. nationals to use their U.S. passport when travelling to/from the United States, regardless of what other passports or nationalities you may possess.
Note that they won't ask you to do this until they've confirmed that every other detail of your application process will pass the requirements, so there's no risk of you renouncing your citizenship and then finding out that you won't be receiving Japanese citizenship. Even so, some countries have a "safety boomerang" clause for their renunciation procedure. For example, if citizens of the United Kingdom renounce their citizenship but do not manage to acquire another citizenship within six months, their U.K. citizenship is automatically restored.
For the case of nationals from the PRC (People's Republic of China), the Chinese Embassy will issue you a special travel letter document that will allow you to travel to Greater China (meaning not Taiwan, Hong Kong, or Macao) during the period where you've renounced your Chinese citizenship and cancelled your CN passport but you have not received your Japanese citizenship and passport yet. This document will not allow you to travel to any other country.
For Americans, there is a time when you apply for relinquishment of your U.S. citizenship and you send your U.S. passport to the State Department for processing. However, as you as still technically a U.S. citizen until the U.S. State Department has issued you a CLN (Certificate of Loss of Nationality), you are issued a letter from the embassy explaining that you are in the process and your U.S. passport is in possession of the State Department. This letter is solely for travel to the United States, and America requires those who are U.S. nationals to use their U.S. passport when travelling to/from the United States, regardless of what other passports or nationalities you may possess.
