How to avoid user logout when closing browser with PHP?

Every session is a cookie, but the cookie data is saved on the server instead of the browser, the cookie of a session is as if it were a token

You can use the session_set_cookie_params

void session_set_cookie_params ( int $lifetime [, string $path [, string $domain [, bool $secure = false [, bool $httponly = false ]]]] )

Setting lifetime will increase session time, as it is technically impossible to create an infinite session.

What would look like:

session_set_cookie_params(<tempo em segundos>);
session_start();

However it does not update after the Cookie has been created, so you may have to use setcookie:

session_set_cookie_params(<tempo de vida>);
session_start();
setcookie(session_name(), session_id(), time() + <tempo de vida>, '/');

You can also implement a simple Ajax to keep running a small script, just to keep the session:

Sessao.php

<?php

$tempodevida = 2678400; // 1 ano de vida
session_set_cookie_params($tempodevida);
session_start();
setcookie(session_name(), session_id(), time() + $tempodevida, '/');

Ajax with JavaScript:

(function sessao() {
    var oReq = new XMLHttpRequest();
    oReq.open("GET", "sessao.php", true);
    oReq.onload = function () {
        //Após o Ajax terminar a requisição executará daqui 5 segundos
        setTimeout(sessao, 5000);
    };
    oReq.send(null);
})();//Auto executa

With jQuery:

(function sessao() {
    $.ajax("sessao.php").then(function () {
        //Após o Ajax terminar a requisição executará daqui 5 segundos
        setTimeout(sessao, 5000);
    });
})();//Auto executa

However I need to make it clear that this will not affect session.gc_maxlifetime, as this is solved in the back-end by Php itself, you can even try to extend the time by changing php.ini this line:

session.gc_maxlifetime=coloque aqui o tempo limite;

Still it will affect all sessions, which will not always be what you want.

How the browser interprets with session_set_cookie_params and without

Without setting session_set_cookie_params:

With session_set_cookie_params:

That is, when Expires / Max-age is equal to Session it means that when the browser is closed and opens again this cookie will cease to exist, but when the lifetime is set the cookie will have a date to expire and every time you use session the time will be updated.