This is far from a simple question. Did the cop take your dad to the precinct? Is he being held under an ICE hold (meaning the police department has alerted the immigration authorities and they have a limited amount of time to claim him for immigration violations)? How did your father get his real social security number?
The bottom line is that you won't get what you need here because this is highly complex. Your parents should be calling the best deportation defense attorney in your area for a thorough evaluation and a plan of action.
The information offered is general in nature and not meant to be relied upon as legal advice. Please consult an attorney prior to making legal decisions. Visit us at www.tunitskylaw.com. Contact us at 713.335.5505 or email at firstname.lastname@example.org. Veronica Tunitsky offers in-person, as well as telephone and email consultations.
I agree with Ms. Tunitsky, you really should contact an immigration attorney. As with most immigration issues, time is of the essence.
I can tell you generally what happens in the area I practice (Sacramento, Ca). Usually the cops just write them a ticket. If they have a warrant out for their arrest then they run into other problems.
Assuming he doesn't have any previous criminal history, contact an immigration attorney and explore what options might be available to him for obtaining some sort of legal status.
Unfortunately the police can turn him over to ICE simply because he is undocumented. If that happened, retain an experienced attorney right away.
This is not legal advice and a client attorney relationship is not created. For a free consultation call (718)234-5588.