Create an application which simply shows a QTextEdit or QLineEdit as a window such as the one below.

#include <QtGui/QApplication>
#include <QtGui/QTextEdit>

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    QTextEdit edit;
    edit.show();

    return app.exec();
}

Right click in the text area to show the context menu and select an option or click elsewhere in the text area to close the menu. The menu will be closed but the text cursor will remain hidden until text is entered or the window loses and regains focus.

This only appears to affect top level widgets.