No. USCIS does not usually bother to come after "small" fish, i.e. a single individual, unless prior criminal conviction or (severe) fraud suspicion or a "pattern" of either criminal activity. Thus, if none of the above apply to your set of facts, I wouldn't worry.
You are given 33 days during which to respond to a NOID and cure your COS application's "defect".
I strongly recommend you hire an attorney to analyze the facts and help you do this, unless, of course, you want your case to be denied for failure to respond.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
It is possible , depends on the facts of your case
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J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Rarely. In the Detroit area, it is common for ice officers to come to your home if you have criminal convictions that make you removable or you have an outstanding removal order or something else serious. Typically they do not come to people's houses after a routine application denial. A NOID is intended to give you an opportunity to respond to their concerns before it comes to that. Talk to an attorney to find out the best course of action in your particular case.