I find the "When composing and executing such pieces, how does one know when it's over?" question a fascinating one.
I'm currently working with another musician and a technologist that will result in a collaborative piece of music indeterminate in length. It'll always be running, the exact same motifs will never be heard together more than once and you, the listener will choose exactly when you start listening to the piece, for how long, and when you stop listening.
I find the philosophy and the basic technological challenges behind such projects fascinating. When complete, the results will be published on a dedicated web site.
This link will take you to a piece I recorded when these ideas started to form in my head a few years back. While it is indeterminate in a way, it does require manual intervention from the listener. You can decide which loop to play, when, where in the loop you'd like to start it and where in the loop you'd like to stop it.
http://eatsleeprepeat.com/minuspilots_menu_edit.html