On a Russian language internet forum for people living or working in Sweden, Swedish Radio found adverts for fake job positions, addresses, sham marriages, ID cards and driving licenses from the Baltic States and Poland, and other forms of ID.
Swedish personal numbers and ID cards could also be bought or rented out.
According to an acquaintance of Rakhmat Akilov, who carried out this month's Stockholm terror attack, he came to Sweden using a Polish visa he had bought, and later tried to sell fake documents to others.
According to SVT, another man used Akilov's personal information to take a job at Scandic Hotel.
Reporters spoke to a man from a medium-sized Swedish town who offered to rent out his personal number and bank account for 2,500 SEK a month.
"I have documents which I can make available," he said. "This means, to put it clearly, that the contract will be signed with me, while you go and work in peace and quiet and receive the salary."
According to Swedish Radio, the man even put his real, registered telephone number on the advert, meaning he saw little risk that he would be approached by police.
"I think this happens at 70 percent of workplaces I've known," said Danijar, who has worked as a paperless migrant in Sweden for nearly two years. "Among the people I know almost everyone is involved in this."
Danijar is from a Central Asian republic, but is carrying Bulgarian ID which he bought for €1,500, although he claims never to have had to use it.
Another Central Asian man, Tigran, told Swedish Radio that he had worked in Stockholm for 13 years, first using a fake Estonian passport, and then using a fake copy of the LMA-cards given out to asylum seekers, some of which give permission to work.
Ingegerd Widell from the Swedish Tax Agency said that she was taking the revelations seriously.
"This is absolutely not good, and it's not something we are gong to ignore," she said. "That's obvious. Then we need to see if this is something we are already working on or something new we need to get a handle on."