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.
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.
I'm doing a story about the proposed changes being made to green cards, and one of the reasons DHS is giving for recalling green cards without expiration dates is that green cards are often passed on to other people and used in forging identities. I'd like to find statistics about how common this practice actually is, and about the number of fraudulent green cards vs. the number of fraudulent driver's licenses that are circulating in the U.S. Any information would be appreciated; my deadline is Wednesday.