While I understand that money is tight, you really need to sort this out with an attorney, since we would really need to know more to answer.
There is no "grace period" with an H-1B. You are out of status as soon as you either stop working for the sponsor employer OR the visa expires. What there is, is a three year bar to coming back to the U.S. if you accrue 180 days "unlawful presence" - i.e.: stay 180 days past the I-94 expiration and then leave, you are subject to a three-year bar to coming back (a ten year bar for overstaying a year before leaving). You have still overstayed and there is no grace period, but by leaving before the 180 days pass you are avoiding an additional penalty.
The I-94 is generally what controls your status here, not the more formal-looking stamp in laminated into your passport. However, a formal determination by a USCIS officer or judge can terminate status earlier, overriding an I-94 (and starting the clock running on "unlawful presence.")
It is somewhat unusual that you would have an I-94 with an end date earlier than your dependents. Plus, since you now have a petition pending for a new employer, it appears that your employment with the sponsor of the earlier H-1B ended at or before the expiration of your I-94, and technically the H-1B needs to be maintaining status for the dependents to be maintaining status. So, whether your dependents are still in valid status is less than clear.
While they wouldn't necessarily need to renew visa stamps, they may still need to leave and re-enter the U.S. to again be in valid status. Speak to a lawyer to clear this up.
The previous answer is on point. I just want to add that I'm not sure what deadline you are referring to. If your I-94 Departure Record (last issued by customs upon your entry OR your last Form I-797 which contained an I-94 on the bottom) expired on 03/24/2008, then you are already well past 1 year out of status. It is very important that you consult an immigration attorney to review your visa, I-94, and other evidence of your lawful status. If in fact you have been acquiring unlawful presence for over one year, then you would be barred from re-entry for 10 years. The bar is triggered when you depart the country.
I'm surprised that you were admitted only until 2008 and not until 2010. Were you required to obtain a license upon your first entry? USCIS will approve someone for one year until they obtain a license which may be unattainable because of the lack of a Social Security Number.
Note, most out-of-state attorneys can legally help you because we are permitted to practice federal immigration law outside of our state of jurisdiction. Please feel free to contact me for a free initial consultation.
Michael A. Harris, Esq.
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