Any Java objects would needs to be fully serializable. See Saving and Loading Java Objects to MAT-Files in the MATLAB docs (note that fig files are mat files).
Swing objects all carry the following caveat in the javadoc.
Warning: Serialized objects of this class will not be compatible with future Swing releases. The current serialization support is appropriate for short term storage or RMI between applications running the same version of Swing. As of 1.4, support for long term storage of all JavaBeansTM has been added to the java.beans package. Please see XMLEncoder.