when your subscription ends. They have DRM - Digital Rights Management. You find them on songs that that you download from legal all-you-can-download subscription services such as Rhapsody and Napster as well as purchased music from those same services and additonally, iTunes and Zune Marketplace. DRM restricts what you can do with those songs. Among the types of restrictions are what devices you can download them to, how many devices/computers you can download to, and how many times you can burn as an audio cd if you can at all. Additionally on services such as Rhapsody, you aren't allowed to burn to audio cd at all unless you purchase the songs individually or as part of an album. And such services place a time limit on how long you can play these songs for. If you don't renew your subscription, those songs will stop playing. Your new player will need to be synced to Rhapsody at least once a month or so to continue the license to play the songs.
There is a move toward DRM free. iTunes, Zune Marketplace, Rhapsody, Napster, and Amazon.com mp3 do sell DRM-free content that are in either mp3 or in a format that can easily be converted to mp3 (as in the case of iTunes Plus tracks). But this is for purchased content. Subscription content, at least of the all-you-can-download variety, will remain with DRM. That allows the existence and continuation of such services.
There are DRM-free subscription services, though. The two that I know of are eMusic and AudioLunchbox. However, these are not all-you-can-download and have defined monthly limits based on your subscription level. They are in mp3 format and are pretty much limited to independent labels. But sometimes you can find popular artists there when they do special projects outside their labels.