My parents' AOS is currently processing, they already received their advance parole document. However, they are both retired so we did not apply for EAD... In hindsight this seems to have been a mistake.
Question now: can they apply for SSN while their application is still pending?
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source https://www.reddit.com/r/immigration/comments/gsyoor/aos_for_parents_still_processing_i485130_can_they/