green card expired while waiting for renewal

If you filed an I-90 to renew or replace your green card and your green card expired while you're waiting for USCIS to process your application you can request an I-551 stamp on your passport to extend the expiration of your previous green card and use that to travel abroad. 

Can I use the I-797 Receipt as proof of identification for travel? No, not for international travel. If you plan to travel outside of the country you need your actual green card or an I-551 stamp in your passport plus a primary form of ID like your passport or your work permit. 

What is an an I-551 stamp? An I-551 is a green card. An I-551 stamp is a temporary green card extension. 

Where can I get an I-551 stamp? You need to make a phone appointment with USCIS at 1-800-375-5283. The days of making appointments online are gone. Unfortunately the appointment may take months, which defeats the whole purpose.