In the code below, given that amethod has been called. At what point/line is the Object originally referenced by myObject, eligible for Garbage Col
Your idea that the private object may be GC'd right away because no other code is able to access it does have some traction, but this would mess with the general semantics of Java memory management. For example, if that object implemented finalize, and Java semantics clearly dictates when an object is eligible for garbage collection, that finalizer method would be have to be called against the specification.
Also note that the object in turn may reference other objects, with even more complicated possible outcomes. Not to mention the object is reachable by Reflection anytime and it would make no sense for the field to be observed to suddenly change to null even if no code could have made that assignment.
To conclude, there are many reasons why your idea of optimization would not work in the wider picture.