I lost my social security card and I'm a green card holder

Resident Alien identification should be plenty.

From the SOCIAL SECURITY website:


You can replace your Social Security card for free if it is lost or stolen. However, you are limited to three replacement cards in a year and 10 during your lifetime. Legal name changes and other exceptions do not count toward these limits. For example, changes in noncitizen status that require card updates may not count toward these limits. Also, you may not be affected by these limits if you can prove you need the card to prevent a significant hardship.

To get a replacement card:

* Complete an Application For A Social Security Card (Form SS-5); and
* Show us documents proving:
o U.S. citizenship (or immigration status and work eligibility); and
o Identity.
* Take (or mail) your completed application and documents to your local Social Security office.

All documents must be either originals or copies certified by the issuing agency. We cannot accept photocopies or notarized copies of documents.

For more information, see Documents You Need for a Social Security Card.
We will mail your number and card as soon as we have all of your information and have verified your documents. Keep your Social Security card in a safe place. Do not carry it with you.