Many people do this. As long as you are not working for a Korea-based company, being claimed as an employee in Korea, you can fly under the radar. Technically you should be performing only the type of work your visa allows, although if you have fulfilled your contract and have a departing airplane ticket you should not encounter any trouble. Your intent to leave the country is clear and does not exceed a B-2 temporary visa period for your country of origin. You are not taking a job in the Korean market for that time period. This falls in the immigration department's "don't ask, don't tell" category.
If by some chance you decide that you want to call the immigration department to double check, get any answer in writing. You will want a paper trail in the event that you take someone's advice. The Seoul Global Center, while notoriously unhelpful, will provide some advice that is not legally binding and may be a good place to start asking questions if you are so inclined.
If you have been out of the United States for 330 days out of the last twelve consecutive months, you may be able to claim an exemption of your earnings up to approximately US$91,000. This will not apply to the income that you begin earning as a freelancer IF the information you provide for the contract company indicates that your residence for hiring purposes is the United States of America.
As always, there are some very fine lines and nuances here where it will be best to consult with a tax accountant. If you come close to the 330 days, you certainly will want to consult with a tax accountant. If you do not, then it may not be worth the effort. KPMG produces a lovely guide called Taxation of U.S. Citizens Abroad that may be worth a look. If there are any particular elements that seem similar to your situation, you should consult with a tax accountant.
< disclaimer >
I am not a tax or immigration lawyer in any country. This does not constitute legal advice. As always, consult with a professional before flossing your teeth or doing anything that might potentially have long term consequences. < / disclaimer >