I\'ve asked around and done some research
And this is how it looks so far. It is definitely not advisable, especially in the light of new security measures, to leave right after you get the GC because it can be easily proven that you didn\'t intend to work for your current employer when you applied for the GC and thus committed immigration fraud. These charges can be filed any time against you if you change jobs. The likelyhood of it happening is low, but, just for your information, after my co-worker got his GC INS called here to verify that he still works at my company. That was after he got the stamp but before he got the plastic card.
The longer you stay at your current job the harder it gets to argue immigration fraud case. However, should they lay you off, you can freely go and get another job - this was not your fault and no fraud has been committed. This is how I understand it...