When sessions are replicated between cluster nodes, they must be serialized by the sender and deserialized by the receiver. These errors indicate that the application has placed a Java object in the session (in this example, com.example.MyClass), which implements Serializable, but cannot be properly deserialized because of a non-serializable superclass in its class hierarchy.
The object in question is serialized successfully for sending, but java.io.InvalidClassException occurs when deserializing on the receiving (backup) node. The first error in the Symptoms indicates that this occurred while replicating a single session, in which case only that session becomes invalid. The second error in the Symptoms occurs when a node that is starting up receives a session state transfer from an existing node. In this case, deserialization is halted for the entire transfer, so the node replicates only the sessions seen prior to raising this error.