Generally nothing happens to the music. The old label usually keeps the rights to any records that they paid to produce, so they keep making money when those records sell. Sometimes a band will buy the rights to their albums from the old label (or the old label will go out of business.)
Green Day recorded their first albums on an indie label called Lookout Records, and then they signed with a major label before they released Dookie. Since Dookie blew up, lots of people bought their early albums, and that made tons of money for Lookout – but Lookout eventually went out of business and Green Day got the rights to their albums back
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