They say they got their inspiration from a scheme in Stockholm which does the same for people that travel the public transport system without a ticket, news agency TT reports.
They hope enough people will sign up and pay a monthly fee, with the proceeds helping filesharers that get caught by police.
But Henrik Rasmusson, one of the state prosecutors that specialises in bringing filesharing cases to court, says the scheme will not have much of an effect. He says that only a small minority of cases end up with filesharers just getting fines. In most cases they get both suspended prison sentences and fines, and an "insurance" scheme cannot help with the suspended sentences, he told TT.