Some way to detect close tab/browser for all browsers?

Question

There are some way of detecting a close event from tab/browser without close when i click in other links in page or forms and valid for all browser, i tested "beforeunload" and other replies about this topic here and not working, i am testing in Firefox and Chrome This is not working :

window.onbeforeunload = function (event) {
    var message = 'Important: Please click on \'Save\' button to leave this page.';
    if (typeof event == 'undefined') {
        event = window.event;
    }
    if (event) {
        event.returnValue = message;
    }
    return message;
};

Same when i close the tab or the browser is doing nothing; but yes when i click a link