From the State Department:
If you are a foreign citizen temporarily in the United States, and you
lose your U.S. visa, you can remain for the duration of your
authorized stay, as shown on your admission stamp or paper Form I-94,
So at least you can stay, get a new passport, and still depart on that new passport, but when you next leave the country you'll need to replace the visa to be allowed back in.
Note that on that page, there are several steps you should follow as well, in terms of contacting the police, your embassy and that you'll need copies of these discussions when applying for the replacement visa:
For replacement of a visa, you must apply in person at a U.S. Embassy
or Consulate abroad. When applying for the replacement of a visa, you
will need to provide a written account documenting the loss of your
passport and visa. Include a copy of the police report.