If you kill the Java process, Java will no longer be running. If you want the threads to keep running continuously, the Java program must remain active.
Invoking such a program with ant is not usually the way to do it. On Unix-like systems, you would typically run such a program in the background via /etc/init.d startup scripts. In Windows the equivalent would be starting your program as a service, though I m not sure of the intricacies involved in getting Java to run this way.
If you re running something from a concole - how about just not killing it and minimising the console? If you re starting it from Linux (or Cygwin) just append a &
to the end of the command line and the process will run in the background.
Tell us more about your environment, and what compromises you re prepared to put up with (e.g. having a minimised console window sit in the taskbar) and we can help you more. At the moment, the only definitive answer I can give is that "yes - Ctrl-C will kill your program (as intended). If you want it to keep running, don t tell it to stop running." :-)