It doesn't sound like you have any reason to be concerned, unless you know of something in the past that you ARE concerned about and wonder whether ICE knows or not. You can hire an attorney to simply prepare you for and appear at your interview and nothing else. If the worst case scenario happens and ICE tries to detain him, there's a chance that the attorney could diffuse the situation.
I don't think you guys have something to worry about.
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it is not common, but it has certainly happened for example if there is an old deportation order. I once had a case with mistaken identity as well - released next day and supervisor called and apologized and approved the case right away.
But typically if it is a straight forward case, it should not happen. Wonder why you are asking?
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