International Travel Rules
US citizens and permanent residents, as well as asylees who hold valid Travel Documents have to be aware that different countries have different rules regarding entry and exit documents during international travel.
For example, when a person leaves the US, the person does not have to go through exit passport control, which exists in most countries of the world. Such exit passport control verifies if a person who visited the country was there legally, and if there was a violation of the internal laws, the person may have to pay fines and penalties before he/she exists the country, even if he/she is a US citizen.
It means that somebody who holds valid US entry documents, may still not be able to leave a foreign country if the laws of that country were violated.
To enter the US, a person has to be in possession of a valid US passport, or a valid passport of the foreign country and a US permanent resident card; or of a valid Travel document issued by the US; or an advance parole; or a valid passport and a valid US visa… The rules for entry documents for those who are coming to the US can be found here » .
Holders of the US issued asylee Travel documents usually must obtain visas before entering foreign countries. However, there are countries that allow US asylees to enter without a visa: Germany, Panama, and Costa Rico do not require visas for those who hold US issued asylee Travel document. Please note that rules may change, and independent verification is required before travelling to these countries. US asylees should also remember that they may not use any other documents for international travel, except for the US issued travel documents.
Further, in case of expired US issued travel documents, if the documents expired recently, and their holder had a good reason for not renewing the documents in time, US authorities may help to enter into the US. For example, a boarding foil may help a holder of the expired permanent resident card to come back home to the US. An advance parole may help to return those who left the country without prior due authorization, but have a right to come back to the US.