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Yes, Facebook might request that you give them a government ID to assist in verifying your identity and restoring your account. They utilize this data to verify your name or gain access to your account again. This ensures your account is accessed by the true owner and keeps it safe from possible misuse.
Here's how it works:
Use Facebook's guidance: If you are having a problem logging in or if you think that your account has been taken over, Facebook will assist you with recovery.

How to Recover Facebook Account Help

• Avoid scams by acting locally or paying with PayPal
• Never pay with Western Union, Moneygram or other anonymous payment services
• Don't buy or sell outside of your country. Don't accept cashier cheques from outside your country
• This site is never involved in any transaction, and does not handle payments, shipping, guarantee transactions, provide escrow services, or offer "buyer protection" or "seller certification"