As an ex CA DMV employee, regardless of ur immigration status if a person has a SSN they need to provide it to the department, when some is applying for AB60 they sign the affidavit, if they have a ssn they can still get AB60 DL, if a person lose status they go to DMV and ask for AB60 conversion, but still need to provide SSN, as for getting regular DL once ur EAD expires will not happen, every time a DL is issued it checks USCIS records, if USCIS docs are expired nothing will be issued