If you lose your green card or it gets partially or completely damaged, or even stolen, send Application to Replace Permanent Resident Card to USCIS. The application is otherwise known as Form I-90.
You are required to send a copy or the original green card along with Form I-90. USCIS may require some other proof of your identity such as copies of your valid external passport or employment authorization card. If you filed a police report to find your stolen green card, you should send a copy of the police report as well.