Julien Bonneville said he founded TheGuarantors in 2016 to guarantee leases for low-credit tenants and international students. But last year, the company unveiled a service to replace security deposits whereby tenants pay a fraction of the deposit upfront (from 7 to 18 percent) and the company insures damages up to the amount of the deposit.

He said the key to protecting renters was to make sure they know their obligations when using alternative products.

“This is growing fast,” he said. “In the future, hopefully, this will become the new standard, so landlords don’t use outdated ways of collecting security deposits such as cash.”

Mr. Jain said the policies his company advocates, including allowing renters to transfer security deposits between landlords when they move, could help free up billions of dollars tied up in security deposit accounts nationwide.

The City Council recently introduced a few bills aimed at lowering upfront costs for renters, including one to cap broker fees at one month’s rent and another that would allow renters to pay security deposits in six monthly installments. In addition, the tenant protections passed in June included a $20 maximum for application fees.

Councilman Keith Powers, a Democrat who represents parts of Manhattan, said an insurance plan like Rhino’s offered renters more options, but “it’s a new idea and I haven’t studied it enough.”

“I think there is a huge opportunity right now, based both on technology and on good policy, to revisit all these upfront costs to offer flexibility and choice,” said Mr. Powers, a co-sponsor of the recently introduced bills.