If you lose your green card, you are still a permanent resident you don't lose your status.

You must apply for a replacement card by filing Form I-90 Application to Replace Permanent Resident Card.

Losing your green card does not affect your ability to live and work in the U.S. but you need proof of your status.

If you are outside the U.S. when you lose your card, you must contact the nearest U.S. embassy to get a temporary travel document.

If you need proof quickly for a job or travel, you can request an "I-551 stamp" in your passport at a USCIS office.