Can a person be held liable if he borrowed a friends car and the car gets stolen?

Yes. In borrowing the car you assumed all liability for the vehicle, its operation and any accidents you cause while driving it and all damage done o it. . This would include:

• Repair or replacement of any damage
• Replacement if stolen
• Paying all speeding and parking tickets
• Cleaning it if it gets dirty or thrown up in.
• Returning it fully fueled

If you don't cover these then you will loose your friend. If he his no longer your friend he and his insurance company will have no problem with suing you for all expenses plus court costs.