I am a Pakistani citizen on a student visa in the USA. I am on a grace period to leave the country. Just a week before my 60-day grace period ends, I lost my passport. I want to return to my country to avoid an illegal stay in the USA. What are my options?
You will need a travel document to board your flight back to Pakistan. Call the nearest Pakistani embassy or consulate in the USA immediately. They can help you get a new passport or emergency travel document.
In addition to ajd's answer: also immediately contact US law enforcement and immigration authorities.
As a foreign national you are required to have a passport on you, so you're in violation of the law by not having one right now. Not sure how they'll act on that, most likely you'll have to present documentation from your embassy or consulate within a certain time frame showing that you're in the process of obtaining a replacement document to prevent arrest.
We had something similar in Spain, though being from another Schengen country there was no overstay risk. Contact the police, contact your consulate or embassy, and hope for the best.