In O Brother, Where Art Thou?, Everett and the gang all sing into a can and cut a record with the song "Man of Constant Sorrow". Later on in the movie we see the radio owner and another man talking about signing them to a contract, and then later seeing the records being sold(and constantly sold out!) around the state. Did the actual band ever get a contract signed, or see a dime of the record sales?
It's unlikely they made any money from the sales of "Man of Constant Sorrow" that happened during the movie. When they recorded the song originally, they were asked to sign papers, and paid $10 each for the work. Most likely they were signing the rights to the recording over to the station owner in exchange for a quick payment.
The "band" themselves had no idea they were popular until they sang at Stoke's fund raiser, as evidence by the claim that "no one will believe we're a real band", and the shock at the crowd's reaction to their song.
We don't have any idea what happened to them after the end of the movie, but it would be reasonable to expect they eventually got signed to a record contract. The governor would probably have wanted them to keep recording music, if nothing else, so he could continue to ride their popularity. That contract would have covered any future recordings; it's also possible they could negotiate royalties for future sales of their hit song, and the station owner would cave in to keep them happy. But that's just speculation, since the last we know of the boys they're going to go work for the governor.