The application uses RichFaces. There are modal dialogs that use conversation scoped beans and there are requests ("AJAX push") being processed in the background are not to participate in those dialog conversations (logically separate).
I can get the desired temporary conversation by using
<input type="hidden" name="conversationPropagation" value="none"/>
on the page, but after one of these posts was processed, the original conversation will no longer be attached to the dialog that is active in parallel. That's because the conversation id is no longer retained and propagated through the page context. The long running conversation is not terminated (expected) but becomes orphaned (not expected).
I'm attaching the source code for extended version of FacesManager that produces the desired behavior. I think that this should be the default behavior, otherwise propagation mode "none" makes no sense in the context of an AJAX app.