The most that i have found on the issue of green-card fraud/forgery has to do with Department of Homeland Security statistics on identity fraud in their Yearbook of Immigration Statistics.
I offer these years:
I'm not sure how much that helps, to be honest.
This was certainly an obscure question. In such a case, i believe it to be very useful if the questioner (you, reader!) can include sources of what you've already found, which may lead us librarians (or not) to more information that you desire.