Is there a user handle once G4 detected an exception? G4 currently can self - abort, can I can save some information on the statistics already accumulated? May be there is a way, however, I did not found it in the documentation.
Currently there's nothing like this in Geant4. G4Exception is a simple class printing aome diagnostics and aporting the application when invoked. For reasons mainly related to performance, C++ exception handling is not used in Geant4. However, we are planning to extend the current mechanism by introducing the capability of handling G4Exceptions in the run manager and allowing users to define the desired application behavior.
I recognize this is a reasonable requirement. As Gabriele wrote in his comment, a new user hook will be introduced. Unfortunately it is too late to have it in the coming release which will happen in a couple of days. The implementation will be done after the current releaase procedure.
Fixes are in the most recent reference tag of geant4-02-00-ref-01.