The visa is a travel document. It allows you to apply for entry into the US in a particular status. The visa does not grant status.
When a visa is presented at the port of entry, and the person is admitted to the US. That person is given an I-94 entry document. The I-94 lists the person's status within the US and the expiration date for that status. As long as the person acts in a way not to violate that status, or change to a different status, they will continue to maintain that status until the expiration date on the I-94.
If the visa in the passport expires while the person is inside the US (as opposed to the I-94 expiring), that does not affect the person's status. However if the person wishes to travel outside the US and return they will most likely be required to renew the visa.
**This information is of a general nature and should not be relied upon without first consulting with an immigration law attorney. This information is not intended to create an attorney-client relationship.