Can resident alien with expired resident cards apply for social security

They need to speak to an immigration lawyer about this - there are methods for renewing a green card, and such an application might be accepted, even late.

However, the reasons for applying so late should be examined and a strategy for explaining these reasons established, as should the background of both parents - these are no longer simple applications, and USCIS will now runs checks. People simply applying to renew a green card can sometimes end up in removal proceedings, if a check reveals a crime of certain types or another reason they would no longer be eligible - even if they were clearly eligible for the green card at the time they were first approved.

Also, the citizenship of their parents should be reviewed to see if there might be automatic citizenship eligibility (probably not of they naturalized later, but worth checking).