It could be worse: The I.R.S. could tax the premiums multiple times — once by disallowing them as a deduction and again as income in the captive — and add penalties of as much as 40 percent on the unpaid tax. The agency is coming off three victories in tax court against captive insurance companies, and the announcement suggests that this deal is as good as it is going to get.

“In the worst-case scenario, you could get hit with a 240 percent tax,” said Jay Adkisson , a lawyer and former chairman of the American Bar Association’s committee on captive insurance companies. “I frankly don’t think anyone who gets this offer is going to reject it, and if they do, they need to find better professionals to advise them.”

Many captive insurance companies are legitimate. They are often used by large companies to self-insure or cover risks that would otherwise be too expensive to cover in the regular insurance market.

Some small captives, known as micro-captive insurance, exist for legitimate insurance needs. A doctor’s office can use captive insurance to pay malpractice claims itself, for instance, or to cover excess claims not paid by traditional insurance policies. In this example, the office would not have to pay all the money it contributed to be in compliance; it would just have to operate as an insurance company and pay some claims.

At issue are captives established as tax-avoidance vehicles. The small-business owners who set them up were able to contribute tax-deductible premiums of $1.2 million a year until 2017, when the limit rose to $2.2 million under the Trump administration tax overhaul and was indexed to inflation.

The I.R.S. offer could put an end to a lucrative structure whose economic advantages seemed to overtake its intended purpose.

“It’s the end of the easy captive,” said John Colvin , a lawyer in Seattle specializing in tax controversies. “Going forward, it’s going to be a niche or specialty thing and not something more broadly based and sold to every person.”