Joshua Smith, a Rockland County insurance broker, was deluged with questions from clients after regulators said they were shutting down Health Republic Insurance of New York, which was known for having some of the lowest rates in the state.

“It’s been a week of craziness,” said Mr. Smith, who owns Vanguard Benefit Solutions LLC, which enrolled about 75 small businesses in Health Republic’s plans. “Lots of emails, lots of calls, and everybody is nervous about what is going to happen.”