If a band was to cover a song on an album, the payments would go to the owner of the rights. This might or might not be the composer(s). If a band covers a song in concert then royalty payment is due again to the owner of the rights. Why might not the composers collect money? At some time in the past the rights might have been sold, particularly when an act has just been signed by a record company. The money is usually collected by rights collecting organisations such as PPL in the UK, or, ASCAP in the USA. Many older musicians look forward to their quarterly payments from these bodies, particularly if Scorsese has used their music to soundtrack a film.