Do I apply for Offer in Compromise as an individual or business?

You should be doing this individually for the civil penalty. You confusion is you think it is just filling out a form. You need a good tax attorney. Ron Cappuccio

You should have some assistance because this is not just a plain vanilla offer in compromise. It's not clear if you were in business as sole proprietors, in which case you're directly responsible, or if the business was run by a corporation and these taxes were assessed out against you as responsible persons. In any event, I am assuming you've been assessed personally and that the OIC is for your personal liability. In that case you would be filing in your own name and not in the business' name. You may want to indicate on a statement attached to the OIC form that the business is closed and list what, if any, of the business assets still exist. If you have new employment, then you would list that in the employment section, generally speaking. If you're unemployed, then you would fill out the form to reflect that.

An offer is compromise is not a simple matter. You only have one chance to negotiate your debt for particular tax year/s. As other attorneys pointed out, an answer to your questions depends on your specific circumstances. If you are delinquent on taxes for LLC or other business entity, you should complete Form 433-A (OIC) (individuals) and 433-B (OIC) (businesses) and provide all required documentation as specified on the forms. There are other details that may be addressed by a tax attorney, such as allowable deductions and allowed business and personal expenses.