Is having an extremely low income a way for a parent to avoid child support?

Very low income may be a way to deviate from or modify the child support award, but in almost all states at least some child support will be due. In some states there is a monthly minimum amount specified, often $50 per child. In other states, there may be a minimum amount (often $20 to $50) that cannot be modified. In a third scenario, in some states, a judge’s discretion still enters the equation. The judge may throw out the guidelines and use his or her knowledge and experience based on the information presented at the modification hearing.

As discussed in an earlier question, the statutory minimum is a way to make certain that parents retain some interest in their children’s lives.

Almost all states have the idea of the "self-support reserve," that is, the minimum amount that a person needs to survive. In this type of scenario, the self-support reserve is subtracted from the income, and the resulting figure is used to calculate the child support award.

As noted above, states have no interest in "punishing" a parent financially via a child support award. A lawyer consulted through state legal aid may be the best person to advise you in this situation.