Demos proposed using the £270 million a year saving to introduce a more contributory principle - giving up to 226,000 people a £23-a-week boost in Jobseeker's Allowance and helping "restore public support" for the welfare system.
Deputy director Duncan O'Leary said the proposals would tackle the 'nothing for something' problem - when people have contributed for many years but find themselves entitled to just £71.70 per week when they lose their job.
"Increasing that figure to around £95 for contributors would send an important signal and help restore public support for welfare," he added.
The idea of introducing a contributory element to welfare has been floated by senior Labour figures, Ed Miliband declaring in 2011 that reforms should ensure it "embodies responsibility and contribution as much as need".
It is also reported to have been among ideas put to voters in marginal constituencies by the Conservatives.
Instead they would be auto-enrolled onto mortgage payment protection insurance. That would cost them around £33 a month if they chose to be covered, the think-tank said - less than the average monthly mobile phone bill.
It also proposed reducing explicit out-of-work benefits for the disabled to the same level as paid to other unemployed people - with the cash moved instead to help with living costs.
Employment Support Allowance would match the two-tier JSA system and savings would pay for a boost to Personal Independence Payments (PIP).