Can a prefix be never routed on Internet but used only for source address in IP packets?

Question:  Can a prefix be never routed on the Internet but used only one-way for source address in IP packets? That is. a user owns an IP prefix. They never advertise a route to it in BGP on the Internet. But they use the prefix solely for source address in IP traffic from a source to a destination (sink).  In this set up, the destination server obviously cannot/doesn't return any acknowledgements etc. to the source.  Anyone aware if there is any such known application in use on the Internet - even if it is rare? Thanks. Sriram