Realistically when you buy music from the likes of Napster, you're not buying the music as such, you're only buying the rights to play it on a computer. Much like when you buy a CD from a shop, you're only buying the right to play it at home, you're not buying the music.
Therefore legally, the music stays with the computer you download it onto unless you pay extra to hear it on something else. This is the whole point of the whole Digital Rights Management argument, to prevent copying. However if you miss a Napster payment, you have no music at all as none of what you've downloaded will play.