Or is it even possible? He has a daughter who's mother is a US citizen and possibly a child on the way
There is no way of getting another work visa once you have accrued unlawful presence. It sounds like he may qualify for family based immigration if he were to marry the mother of his child-for all of the right reasons of course. See at attorney for a more detailed explanation.
You cannot obtain a change of status from one nonimmigrant classification another if your status has lapsed. In certain circumstances, you may be able to apply for a new visa overseas, however, the person may be barred from readmission due to unlawful presence. HE needs to consult with an immigration attorney directly.
Employment / Labor Attorney
No change of status for those who fell out of it. Other options might be available: Adjustment based on VAWA, marriage to the US citizen, maybe U visa, asylum, but not another work visa...
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