The scam artist's goal is to steal your money, steal your identity or both. In fact, don't carry anything with your Social Security number on it, and don't offer it to anyone unless it's for tax, employment or credit purposes.
There are other ways scammers and identity thieves can get your valuable financial information – for instance, by hacking into a merchant's system and lifting your (and hundreds of other customers') debit card pin numbers.
So be sure to monitor online bank and brokerage accounts a few times a week, and if you see any suspicious withdrawals or charges, report it to your financial institution.