Frequently Asked Questions - Form I-131
They will enter the USA as permanent residents. The duration of the immigrant visa is stated on the visa stamp (I think it will be 6 months) and they must enter the USA within that time. They can come and leave after they get their green card in the USA.
Make an infopass appointment and get her passport stamped for temporary proof of green card. She can travel with that. Normally, the physical GC takes just a few weeks. I am not concerned about SSN. That will arrive eventually. But do review my blog videos about I-131 and maintaining green card, etc.
There has been no change to this policy. USCIS requires documentary evidence of the emergent situation, as well as supporting documentation indicating that the applicant has a pending application.
As I recall, as long as the application has been physically received by USCIS, your departure does not cause abandonment. So, you should not have to worry. But you will need to be back for biometrics associated with the I-131.