If a Thread creates a daemon Thread, can I rely on the fact that when the parent exits the run method, the son will also terminate?
No - threads are independent. There's no sense of one thread "owning" another and forcing termination.
If you're really asking whether when all the non-daemon threads in the application have died, you can rely on the process dying: yes, you can. But that's all you can rely on.
In particular, if there are two non-daemon threads, each of which has created a daemon thread, and one of the non-daemon threads terminates, then the remaining three threads will continue running.
From: http://journals.ecs.soton.ac.uk/java/tutorial/java/threads/daemon.html
When the only remaining threads in a process are daemon threads, the interpreter exits. This makes sense because when only daemon threads remain, there is no other thread for which a daemon thread can provide a service.
I believe daemon threads are tied to the JVM and not the creating thread.