Generally speaking, you can only be held in contempt if you have the ability to satisfy that contempt. From your facts, it appears you do not have the ability to clear the back support. Clearly you need to have a modification of the support, but that is something that needed to be done when your income changed, initially. Even though you are on welfare, a family court is still likely to impute an income to you, based on your ability to work, your education level, and a number of other factors. It may be that the court finds you are only capable of earning minimum wage. Even there, support will still be ordered and you accrue even more back support. But it is unlikely you will be held in contempt, unless you have a way to pay the support.
Yes, seek a modification order to suspend payment
Whether contempt against you will be ordered will depend on factors such a the judge, the judge's mood, the evidence against you, the number of prior times you've been in court on the arrears, etc....
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