The report suggested possible changes to how sick leave is paid
Insurers rather than the government could provide benefits such as sick leave, says a report into the industry.
Setting out a possible scenario for 2020, the report said a 5% shift in the £340bn welfare state burden could save the government £17bn a year.
But consumers would need to take out insurance against sickness and job loss as a result.
The Insurance Industry Working Group was set up in October last year, comprising bosses of major firms.
The UK insurance industry is the second largest in the world.
The group was chaired by Chancellor Alistair Darling and Andrew Moss, the chief executive of Aviva.
It found that the total cost of payouts such as long-term healthcare and pensions cost £340bn a year, with the insurance industry picking up a third of the cost and the government picking up the rest.
The report suggested that the insurance sector had the capacity to play a much bigger role in providing benefits like jobseekers allowance and money for those on long-term sick leave.
Taking on 5% of the burden from the government would save the Treasury billions of pounds, but would mark a fundamental shift in the welfare state, which is funded by taxation and National Insurance contributions.
The report also pointed out that the transparency, simplicity and access of insurance products could be improved.
It also said that data and research could be shared between government and the industry to reduce the cost impact of risks such as floods and crime.
Mr Moss said the report was simply a "discussion document" and was not giving any firm recommendations, but encouraged others to take up the debate.
"Taking steps now will build customer confidence," he said.