Scenario 1: Work + No Pay
Suppose I do work, but do not receive any compensation for the work. This can happen because an employer did not pay me what I was supposed to get paid. It can also happen because I do work that does not get paid, including things like caring for others and domestic labor. Is my poverty reduced by this? No.
Scenario 2: No Work + No Pay
Suppose I do not do work and do not receive any income. This could be because I am disabled and my country does not provide social insurance for disability. Is my poverty reduced by this? No.
Scenario 3: Work + Pay
Suppose I do work and receive pay. Is my poverty reduced by this? Yes.
Scenario 4: No Work + Pay
Suppose I do not do work and receive pay. For instance, I am disabled and receive disability payments. Is my poverty reduced by this? Yes.
Conclusion
It seems that work does not reduce poverty. Only pay does. I can tell this because Pay predicts poverty reduction 100% of the time no matter its relation to Work, while Work only predicts poverty reduction when it is coupled with Pay.