I can think of a variety of protocols that broadcast information and don't really care about whether it gets delivered.. Think of everything that uses UDP on TCP/IP. The most basic thing I can think of would be low-priority notifications that are sent to the entire Bitcoin universe, but don't need to persist. The protocol provides for a signed and thus verified message, and a method for broadcasting it to every node that might be interested in seeing it. If it never makes it into a block, so be it. If it does, so be it.