If you filed an I-90 seeking a replacement card, that will not be affected by your criminal issues. Regarding the status of your residency, it depends on the nature of the final resolution of your criminal cases (i.e. was adjudication withheld, did you enter a guilty plea, were the charges dropped, etc.), which will may or may not become an issue until you seek adjustment of your status to U.S. Citizen.
If you received the greencard prior to the incident and you are fingerprinted in order to get your new card it could cause you some probplems. Shoplifting is a CIMT and a deportable offense. however. you do have defenses to the removal.
You are eligible for NATZ. i suggest that as soon as you get your replacement greencard you apply. Once you are a USC, you will no longer need to worry about issues such as this.
1. no they can not deny your green card,
2. they can keep you from coming back,
3. people convicted of two or more crimes involving moral turpitude are subject to mandatory detention, find an attorney fast. bruce coane of miami is one of the best
The advice that I give in each answer or legal is not intended to take the place of an in person consultation. A complete answer takes an in depth interview. After all, it is a life that is at stake. If you are in another city that I do not service ask me and I might be able to recommend you an attorney there. In general, in Houston, I recommend Adan Vega or Bruce Coane, Specialists. In Dallas I recommend Richard Fernandez, Elizabeth Cedillo or Yong Wood as highly skilled and experienced. In South Texas I recommend Jodi Goodwin from Harlengin or Leonel Perez of Edinburg. In San Antonio I recommend Bob or Nancy Shivers or drive to Austin to see me or my talented associate Jacqueline Watson.
Refuse to issue you a card? No. Place you in removal proceedings? Possibly yes. An alien convicted of two crimes of moral turpitude not arising out of the same criminal scheme is deportable. The crimes do not need to be felonies.
I recommend that you consult with an experienced immigration attorney before taking any action.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.