What is more likely to play out is that assuming that when currently minimum pay for a hour is $10 and tax 0% then with negative tax X and no minimum the pay would become $10 / (1-X/100). The worker will get the same (hopefully) and the company will pay less.
It means the worker has voluntarily participated in selling their labor, even if its for a lower price than they would have made before, and they would always have the option to stop doing it and do something - anything - else.
If the NIT is insufficient to provide the necessities of life than its institution failed in its primary objective, albeit I would still argue any NIT is better than none because it raises the poverty floor some amount above zero.