The BSA regulation requires banks to obtain a "statement of purpose" for loans in excess of $10,000 not secured by real estate. It should be descriptive enough to allow a reviewer to "chase proceeds;" i.e. compare what the applicant said to what the borrower did. If the lie would have affected your bank's decision to make the loan it's a "false statement" and could be classified as fraud. The type of fraud would depend on the purpose of the loan; e.g. business loan, consumer loan, etc. You will either file a SAR or document why you did not.
That's the easy part.
You need to sit down with the borrower and present him with what you know. Depending on the facts and the language in your note and security agreement, one possible result of that conversation would be that your bank calls the loan. Depending on the circumstances, continuing to list the credit on your balance sheet at 100 cents on the dollar could be considered as misrepresenting your income statement.
Filing a SAR never represents a cure of the underlying problem.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.