event.clientX; and event.clientY do not work in firefox

Your code is almost there. Two small changes work out.

In the addEventListener part, reference the function you want to call instead of using an anonymous function and call the other function from there:

document.getElementById(div_barra_id).addEventListener("mouseout", move_janela_mouse, false);

This type of listener association will automatically pass an event object as the first argument of the function. So just change the first line of the function to:

function move_janela_mouse(event) {
    ...

You can assign the values to the variable in this way

var xMouse = event.clientX || event.pageX;
var yMouse = event.clientY || event.pageY;

In short, if the first one does not run, it goes with the second value

Here's a suggested improvement for your code. this way you create a scope for your variables and avoid unnecessary calls to the mouse event.

var MoverJanelaInicial = function (div_barra_id) {
    // iniciando variaveis que serão utilizadas no evento.
    this.elemento = document.getElementById(div_barra_id);
    this.elemento_body = window.parent.document.getElementById('corpo_main');
    this.boxDoElemento = this.elemento_body.getBoundingClientRect();
    this.elemento_move = document.getElementById(window.parent.document.getElementById(div_barra_id).parentNode.id); 
    this.maximo_top = this.elemento_body.offsetHeight - this.elemento_move.offsetHeight;
    this.maximo_left = this.elemento_body.offsetWidth - this.elemento_move.offsetWidth;

    // no lugar de temos uma variavel "mover" controlando à chamada do evento "mouseout".
    // que tal apenas remover a associação do evento após executa-lo?
    // para tal é preciso guardar uma referencia ao evento.
    // o ".bind(this)", serve para trocar trocar o objeto de contexto do evento, desta forma o this deixa de ser o elemento DOM e passa a ser à instancia de MoverJanelaInicial
    this.onMouseOut = this.moverJanelaMouse.bind(this);
    this.elemento.addEventListener("mouseout", this.onMouseOut);
}

MoverJanelaInicial.prototype.moverJanelaMouse = function (event) {
    var rolamentoX = this.elemento_body.scrollLeft;
    var rolamentoY = this.elemento_body.scrollTop;

    var xmouse = event.clientX;
    var ymouse = event.clientY;

    var px = ((xmouse - this.boxDoElemento.left + rolamentoX) - (this.elemento_move.clientWidth / 2));
    var py = ymouse - this.boxDoElemento.top + rolamentoY;


    if (py < 0) 
        py = 0;
    if (py > (maximo_top - 50)) 
        py = (maximo_top - 50);

    if (px < 0) 
        px = 0;
    if (px > maximo_left) 
        px = maximo_left;

    this.elemento_move.style.left = px;
    this.elemento_move.style.top = py;

    // removendo evento "mouseout"
    this.elemento.removeEventListener("mouseout", this.onMouseOut);
}

// instanciando o objeto
var moverJanela = new MoverJanelaInicial("meu_id");

Thank you for the tips, without them you would not have been able to. Several of them could not be used because I wanted to create a function that could be called from anywhere in my project, just referring to it in ondragstart, without passing any id or worrying about other events. The way below works perfectly in firefox and chrome. If you do not want to do this, you can use the following code: