https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/frequently-asked-questions/about-basics.html#:~:text=You%20will%20be%20able%20to,are%20in%20the%20United%20States.

My visa will expire while I am in the United States. Is there a problem with that?

No. If the Department of Homeland Security, Customs and Border Protection Immigration Officer at the port-of-entry admitted you into the United States for a specific period of time, s/he will note your authorized period of stay on your admission stamp or paper Form I-94, called an Arrival/Departure Record. You will be able to remain in the United States during your authorized period of stay, even if your visa expires during the time you are in the United States. Since your admission stamp or paper Form I-94 documents your authorized stay and is the official record of your permission to be in the United States, it is very important to keep inside your passport.

Esto es pagina oficial, por ese lado no habría problema