This is one of a difficult and tricky questions and answering this correctly would mean you are an expert in Java Serialization concept. In an already serialized object, the most challenging task is to change the structure of a class when a new field is added or removed. As per the specifications of Java Serialization, addition of any method or field is considered to be a compatible change whereas changing of class hierarchy or non-implementation of Serializable interface is considered to be a non-compatible change. You can go through the Java serialization specification for the extensive list of compatible and non-compatible changes. If a serialized object need to be compatible with an older version, it is necessary that the newer version follows some rules for compatible and incompatible changes. A compatible change to the implementing class is one that can be applied to a new version of the class, which still keeps the object stream compatible with older version of same class. Some Simple Examples of compatible changes are:

Addition of a new field or class will not affect serialization, since any new data in the stream is simply ignored by older versions. the newly added field will be set to its default values when the object of an older version of the class is un marshaled.
The access modifiers change (like private, public, protected or default) is compatible since they are not reflected in the serialized object stream.
Changing a transient field to a non-transient field is compatible change since it is similar to adding a field.
Changing a static field to a non-static field is compatible change since it is also similar to adding a field.
Some Simple Examples of incompatible changes are:
Changing implementation from Serializable to Externalizable interface can not be done since this will result in the creation of an incompatible object stream.
Deleting a existing Serializable fields will cause a problem.
Changing a non-transient field to a transient field is incompatible change since it is similar to deleting a field.
Changing a non-static field to a static field is incompatible change since it is also similar to deleting a field.
Changing the type of a attribute within a class would be incompatible, since this would cause a failure when attempting to read and convert the original field into the new field.
Changing the package of class is incompatible. Since the fully-qualified class name is written as part of the object byte stream.

Java serialization is one of the most commonly misunderstood areas. Many developers still think its only used for saving objects on the file system