Many people often misuse the word "visa". Within the U.S. immigration context, a visa can only be issued by a U.S. Embassy or Consulate outside the U.S. The visa is the document which is placed in the passport. It merely allows a foreign national to enter the U.S.
When a foreign national with a visa arrives at a U.S. port of entry, he or she must present that visa. Upon being admitted to the U.S. with that visa, the foreign national is granted a status. For example, when a foreign national arrives at a U.S. port of entry with a B-1/B-2 visitor visa with the intention of being a tourist, that foreign national may be admitted to the U.S. in B-2 status. That status will likely be valid for 6 months. If, during his or her stay the foreign national decides to stay longer than 6 months, he or she can apply for an extension of status.
Assuming that a foreign national within the U.S. maintains his or her status, it does not matter if his or her visa expires, so long as the foreign national does not travel outside the U.S.