PineDev

You need to move closing tags of the parent element to end_el() method override.

E.g. in your case:

function start_el(&$output, $item, $depth, $args) {
    global $wp_query;
    /*
     * Генерируем строку с CSS-классами элемента меню
     */
    if($depth == 0){
        	$class_names = 'header_nav-link_wrap';
    	}else{
    		$class_names = '';
    	}
        !empty ( $class_names ) and $class_names = ' class="'. esc_attr( $class_names ) . '"';
        if($depth == 0){
        	$output .= "<div $class_names>";
        }else{
        	$output .= "";
        }
        
        $attributes  = '';
        if($depth == 0){
        	$attributes .= 'class="header_nav-link"';
        }else{
        	$attributes .= 'class="header_nav-sublink"';
        }
        !empty( $item->url ) and $attributes .= ' href="'   . esc_attr( $item->url        ) .'"';
        $title = apply_filters( 'the_title', $item->title, $item->ID );
        
        $item_output = $args->before
          . "<a $attributes>"
          . $args->link_before
          . $title
          . '</a>'
          . $args->link_after
          . $args->after;
        
        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
  }

  function end_el(&$output, $item, $depth, $args) {
        if($depth == 0){
        	$output .= "</div>";
        }
  }