Php pdo Select statement that returns an array and that array is used to query the database again

Use a single query using two JOINS.
You can "use" the same table twice by giving it unique aliases within the query so any reference to that table is unambigious.
As mentioned in the comments to your question, this won't work for temporary tables with MySQL. Therefore the following example does not use CREATE TEMPORARY TABLE.... in the setup() function. I usually try to avoid that. So, keep in mind that this example might overwrite exsting tables (though I hope the table name is quite unique) and it persists data on your database server.

<?php
$pdo = new PDO('mysql:host=localhost;dbname=test;charset=utf8', 'localonly', 'localonly');  
//echo 'client version: ', $pdo->getAttribute(PDO::ATTR_CLIENT_VERSION), "\n";
//echo 'server version: ', $pdo->getAttribute(PDO::ATTR_SERVER_VERSION), "\n";
$pdo->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
$pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);
setup($pdo);


$stmt = $pdo->prepare('
    SELECT
        u2.user_id
    FROM
        soNOTTEMPUsers as u1
    JOIN
        soNOTTEMPFriends as f
    ON
        u1.user_id=f.user_id
    JOIN
        soNOTTEMPUsers as u2
    ON
        f.friend_id=u2.user_id
    WHERE
        u1.username=:username
');

$stmt->bindParam('username', $username);
foreach( array('userA', 'userB', 'userC', 'userD') as $username ) {
    echo 'querying friends of ', $username, "\r\n";
    $stmt->execute();
    foreach( $stmt as $row ) {
        echo '  ', join(', ', $row), "\r\n";    
    }
}

function setup($pdo) {
    $queries = array(
        '
            CREATE TABLE IF NOT EXISTS soNOTTEMPUsers (
                user_id INT,
                username varchar(32),
                primary key(user_id)
            )
        ',
        '
            CREATE TABLE IF NOT EXISTS soNOTTEMPFriends (
                user_id INT,
                friend_id INT,
                primary key(user_id, friend_id)
            )
        ',
        "REPLACE soNOTTEMPUsers (user_id, username) VALUES
            (1, 'userA'), (2, 'userB'), (3, 'userC'), (4, 'userD')
        ",
        "REPLACE INTO soNOTTEMPFriends (user_id, friend_id) VALUES
            (1,2),(1,3),(1,4),
            (2,1),(2,3),(2,4),
            (3,1),(3,4),
            (4,1)
        ",
    );
    foreach( $queries as $q ) {
        $pdo->exec($q);
    }

}

prints

querying friends of userA
  2, 2
  3, 3
  4, 4
querying friends of userB
  1, 1
  3, 3
  4, 4
querying friends of userC
  1, 1
  4, 4
querying friends of userD
  1, 1

as expected (though not tested for consistency like a friendof b <=> b friendof a)

PLease change your code with following code

$stmt = $dbh->query("SELECT user_id FROM users WHERE username = '" . $user_name . "'");
    $row = $stmt->fetch(PDO::FETCH_ASSOC);
    $user_id = $row['user_id'];

    $stmt = $dbh->query("SELECT friend_id FROM friends WHERE user_id ='" . $user_id . "'");
    $ret_array = $stmt->fetchAll(PDO::FETCH_ASSOC);

    for($i = 0; $i<count($ret_array); $i++) {
        $stmt = $dbh->query("SELECT profile_path, username FROM users WHERE user_id=" .$ret_array[$i]['friend_id']);
        $show_all_friends[] = $stmt->fetchAll(PDO::FETCH_ASSOC);
    }


    return $show_all_friends;

Hope this helps