Lawyer here, If someone entered the United States without inspection, was deported, and then re-entered the country again without permission, they are subject to a 10-year bar. INA § 212(a)(9)(C) states that an individual cannot apply for permission to re-enter the United States until 10 years have passed since their last departure. He is inside the U.S, but there is no waiver available while he is inside the U.S.
To overcome this, he must remain outside the United States for a full 10 years. Once the I-130 is approved, he will need to apply for a waiver to overcome the inadmissibility and proceed with immigrant visa processing.