You most probably don’t need to file Form I-131A, Application for Travel Document (Carrier Documentation), or Form I-131A, if you are not present in the USA and your green card expired.
According to the rules of Customs and Border Protection policy, a transportation carrier destined for the United States is allowed to board the permanent residents who do not have carrier travel documentation if they possess: an expired 10-year green card or expired 2-year green card together with a valid Form I-797 (Notice of Action) confirming the status extension.
If you are the owner of one of these documents, it is possible to use them for returning to the USA, without filing Form I-131A. Nevertheless, it is recommended to ask a transportation carrier in advance whether these documents are accepted.
If your green card or re-entry permit was stolen, lost, damaged or destroyed abroad, it is compulsory to file Form I-131A, otherwise a transportation carrier would not permit you to board, and your entry would be definitely refused by the Customs and Border Protection officer.
An expired green card cannot be renewed outside the USA, which means you must submit Application to Replace Permanent Resident Card (Form I-90) in order to replace your green card after coming back to the United States.
Moreover, green card holders who were absent for one year or more in the United States (or two years if they have valid re-entry permit) are not eligible to file Form I-131A, as their permanent residence might be abandoned.
February 7, 2019