1) Most important, don't let your LP work for that consulting company. If she cheated INS, e.g., earning money as F1 or making fake documentation, there would be tons of trouble in the future.
2) As you have GC, can you apply GC for her? I don't know enough immigration law. There are quite a few Chinese immigration lawyers around US, who can help you to figure something out. (Xiaobaitu on this forum knows a lot.)
3) If there is difficult to hold your LP's status, I'd rather send her back to school to be on F1. For your situation, working illegally is the worst thing you can do now.
4) You need to check the document your LP signed with the company. Normally, there should be no problem to quit a job.
Good luck!