Green Card holders are legal residents of the United States and people who hold such residents cards can lawfully work in America and stay in any American state. These Green Card holders can also travel abroad for work purposes or for vacation, but their stay in a foreign country must not be a lengthy one. To travel abroad, without losing their lawful status in America, Green Card holders will have to obtain re-entry permits. Nevertheless, a Green Card by itself is a travel document and Green Card holders can travel abroad for a certain period of time with their Green Cards and they need not obtain any other travel documents to travel abroad.
However, being a Green Card holder, in certain circumstances, you may be required to obtain a travel document to travel to a foreign country and if you need to remain in a foreign country for an extended period of time, you will have file Form I-131, Application for a Travel Document, prior to leaving the country and obtain a travel document, to get back to the country hassle free. Being a United States Green Card holder, if you look forward to live in another country temporarily for less than two years, you will have to file Form I-131, ahead of your departure and get a re-entry permit and this permit will help you to travel abroad and get back to the United States. Nevertheless, you will have to demonstrate that you need to remain in a foreign country for a prolonged time period due to a genuine reason as Green Cards are issued to people who wish to settle in America and if you plan to settle in a foreign country permanently, you will be stripped of your lawful status in America.
If you were granted refugee or asylee status in America and if you had obtained a Green Card after living as a refugee or an asylee for one year in America, you will have to obtain a refugee travel document to travel abroad. If you need to remain in a foreign country for less than six months, you need not obtain a re-entry permit and you can travel with your Green Card. At the same time, you will have to get back to the country before your re-entry permit expires. Green Card holders can travel abroad with their Green Cards and passports from their home countries. However, they cannot travel abroad if they hold expired Green Cards or if their Green Cards are invalid.