I think the agreed upon solution is to use a static browser listener. Something like what I've shown below. Note that you might need to check whether the browser count is 1 instead of 0 depending on when the count is decreased.

  // import com.borland.primetime.ide.Browser;
  // import com.borland.primetime.ide.BrowserListener;
  Browser.addStaticBrowserListener(new BrowserListener() {
    public void browserClosed(Browser p0) {
      if (Browser.getBrowserCount() == 0) {
        // JBuilder is exiting.  Do something about it.
      }
    }

    public void browserViewerDeactivating(Browser p0, Node p1, NodeViewer p2) throws VetoException {}
    public void browserViewerActivated(Browser p0, Node p1, NodeViewer p2) {}
    public void browserNodeClosed(Browser p0, Node p1) {}
    public void browserNodeActivated(Browser p0, Node p1) {}
    public void browserProjectClosed(Browser p0, Project p1) {}
    public void browserProjectActivated(Browser p0, Project p1) {}
    public void browserClosing(Browser p0) throws VetoException {}
    public void browserDeactivated(Browser p0) {}
    public void browserActivated(Browser p0) {}
    public void browserOpened(Browser p0) {}
  }