This is one of those questions where the answer may seem obvious at first glance but it is difficult to answer without elaborating.
When you submit your I-485 application, you are at the final leg of the years-long journey to permanent residency in the U.S. As part of the green card application package, you may also submit I-765 (EAD) and I-131 (advance parole) together with your green card application (I-485). While your green card is pending, the EAD allows you to work lawfully with any employer and the advance parole allows you travel overseas. If you apply for both, you would receive what’s commonly referred to as the “combo card”. The combo card is generally issued in about 4 months after filing your application package.
If you are in H-1B status at time of filing your application package, you are not required to maintain that status until your green card is approved. The law only requires you to have status at time of filing. With the EAD or Combo card in hand, you could work lawfully with your current H-1B employer even after your current H-1B status expires. The initial EAD/Combo Card lasts for one year and may be extended in one year increments as long as the green card remains pending. As such, many do not see the relevance of H-1B after they’ve filed for green card which is true in most respects.
But it is a good idea to keep your H-1B alive to protect yourself in the rare event that I-485 is denied. If it happens, it’s likely due to an inadmissibility issue (criminal conviction, communist party membership, misrepresentation, etc) or a status issue in your immigration history. For family based I-485s, your marriage may suddenly end. Or, an overzealous officer may deny your I-485 by applying the law incorrectly.
Without H-1B status at time of your denial, you would not be deemed to have lawful presence in the U.S. Your EAD would be deemed invalid at time of the denial, and as such, you will immediately lose work authorization. This means that if you want to return to H-1B, you would need to travel overseas and go through consular processing. And consular processing has its own problems including unexpected delays which may create additional disruptions at home-making meaningful planning impossible.
If you hold H-1B status at time of green card denial, you may continue to stay in the U.S., and possibly plan to re-file. You may also continue to work with your current employer or become a beneficiary of a transfer petition if you decide to change job. Having H-1B status to fallback on eases stress and allows you to re-group and figure things out while remaining in the U.S.
In even rarer situations, it’s helpful to have H-1B if sponsoring employer decides to terminate your employment immediately after you’ve filed for green card. In this scenario, you have not received EAD or combo card yet but your H-1B has already expired. Anyone stuck in that scenario would be focused on finding a new employer to port the pending I-485 (available to EB1, EB2, and EB3 categories). It certainly would make you more marketable if you have work authorization already. Waiting for EAD or combo card to arrive is nerve wracking especially in such desperate time. And there is no guarantee when it’ll arrive, sometimes lasting a year or more.
Ultimately, it’s not your call to make as filing the H-1B petition is your company’s decision. But if you have a role in the decision making process, hopefully this post would guide you to reach the right answer for your situation.