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I asked similar questions to my lawyer. Her answer was :
"INS and FBI will check your records under two cases - criminal investigation and adjudicaition of citizenship applications."
"Since GC is based on permanent employment for most of us, if we quit as soon as we get GC approval, when INS looks at your job records due above mentioned reasons, they might deny citizenship or worse still, they might revoke your GC. This is a gray area and no one know how INS is going to interpret it going forward (especially in light of the 180 days rule). "
Hope this is helpful. Pl. do not take this as legal advice. Check with a competant immigration lawyer.
-Raju