If she doesn't have GC or re-entry permit, she'd have issues coming back to the US. She may need to relinquish her LPR status and start from scratch when ready to move to the US.
I don't believe there's many options for maintaining status in this situation, but others can advice.
If she already had GC in hand that would be a risky move, but she could try leaving without approved re-entry permit, after doing biometrics for it.