one thing that are available that may apply to you right now are DACA, deferred action for childhood arrivals, if you qualify for this you can receive a work card. Other than that, us lawyers rely upon you to gain the family relationship you need to qualify for immigration benefits. Good luck.
I am a pretty smart guy, but I do not know everything. My answers here come from the knowledge I carry around in my head--if you want me to look something up, you should come see me. Take any advice here as being general in nature. Please be careful with your life and make decisions that are smart.
A common misconception is that an employment authorization document (EAD) or 'work permit' can be obtained alone without any underlying process, or application. You have to have some way to apply for status or otherwise apply for some type of relief, such as DACA or other process. Your question does not contain sufficient facts to enable an attorney to determine what , if any, relief you may have. If you seek a confidential consultation you may be able to obtain advice which would provide you answers. Seek help now in a confidential setting. Good luck
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You really need to discuss your situation with an attorney. Lots of info we would need to know to advise you.
First question is what you mean by a "work permit" - different things allow a person to work: US citizenship, US permanent residence (a "green card"), various non-immigrant work visa (normally limited to specific employers), or an Employment Authorization Document (there are many, many ways a person can qualify for an employment authorization document, but you need to fit into one of these ways - not everyone does, and you can't simply apply for one unless you do).
Next, what is your current situation? Not just that you have been working without authorization, but how did you first enter the US? What is your family situation? If not in status, have you simply violated status or are you subject to an unlawful presence bar?
Chances, are almost anything (but not everything) done to get back into status would require you to process outside the US, and if you have enough unlawful presence time you may be barred from returning.
You really need to speak with a lawyer to figure out where you stand.