still no comments on this? i thought it's a simple question and should be one of the basic features of seam bijection
The documentation is probably quite sufficient to answer your own question. Also your own experiments have answered your question too.
Once you end a conversation all state in that conversation is gone. (Not immediately but, for the sake of keeping this simple let's just go with it). And by definition a parent should not inject a nested conversation variable as this could lead to inconsistent behaviour during conversation switching and ending IMO. Nested conversations is not the most well defined part of the Seam framework and for that reason I never write my conversations as nested. But, that's another story.
So you have 2 options. Use the Session context which is generally not ideal but it works and as long as your careful with cleaning up it will probably be good enough.
When in a nested conversation you still have access to parent conversations. So, instead of trying to @Out(ject) the variable just set the state you want on a Seam bean in the parent conversation before ending the nested conversation.