I am not sure if I understand your question correctly.
What I can say is that the EJB container only makes sure that a bean instance is associated with only one
thread at a time.
A static field can still be accessible across all threads. So thread A (associated with EJB instance A) can start a transaction and access and modify the static field. Simultaneously thread B (associated with EJB instance B) can start another transaction and access and modify the same static field at the same time.
Hope that helps !