Although this isn't an immigration question and you should talk to an unemployment lawyer ... it is my understanding that you can not get unemployment if you don't have a work permit ... one requirement for unemployment is that you are ready-willing-and-ABLE to work and have been making applications for work.
As for food stamps, I think you need to be lawfully in the US .. again, I'm not certain.
BUT,the good news is that the US citizen children may qualify for government welfare/food benefits.
Go talk to someone at a local Legal Aid office.
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ICE does not put people in removal proceedings and revoke Humanitarian parole just so, out of no reason. If want an answer to your question, reach out to an immigrant attorney, disclose your facts in entirely and maybe you will get an answer or maybe even a solution to your problem.
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