I have actually been trying to brainstorm how some may get over this problem and have come to only 3 conclusions thus far.

1.Try gaining National ID from your country of origin.

2.Use your last expired passport and try to get a copy of the passport regulations from your Home country which highlight why you can't currently renew it.

3.Asking for an Emergency passport.I'm pretty sure the requirements would be pretty much different in trying to gain such a document if possible but the Dreamer in question should research their own countries rules BEFORE attempting this obviously!!!

It is very likely the Deferred action process AND The biometrics portion of the EAD will require a form of government ID.