It could also happen that more people decide not to bother with work, reducing the supply of labor and increasing the cost of labor (aka wages).
Getting paid less is a fine outcome assuming the NIT fulfills its purpose of guaranteeing a minimum standard of living.
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.
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.