Secret Chiefs 3 come to mind. They recently started selling ‘Geek Pack’ downloads for some of their songs. It’s a folder containing the hi-res stems for a given song. It also includes detailed notes on the song’s production. For a fan like me, it’s a very welcome look into their process.
A much more common approach is for artists to release an instrumental or vocal acapella to a song. It’s not uncommon for hip hop records to release entire instrumental versions of their albums.
One effect of this is that other rappers are encouraged to take the opportunity to rap their own verses over someone else’s instrumental. This occurs a lot in the tradition of rap mixtapes, which are halfway between albums of original music and riding on someone else’s beat.
ISTR Nine Inch Nails used to do this.