As long as we are talking about HotSpot JVM ...
Object itself IS NOT marked as finalized.
Each time when you create new finalize object, JVM creates an extra object FinalizerRef (which is somewhat similar with Weak/Soft/Phantom references).
Once your object is proven to unreachable with strong references special references to this object are processed. FinalizerRef for you object will be added to finalizer queue (which is linked list, same as with other reference types).
When finalizer thread consumes FinalizerRef from queue it would null its null pointer to object (though thread will keep strong reference to object until finalizer is finished).
Once FinalizerRef is nullified, object cannot get to finalizer queue any more.
BTW
You can see preference processing times (and number of references) in GC logs with -XX:+PrintReferenceGC
(see more GC diagnostic JVM options)
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