Slick slider adds some .slick-cloned divs before and after the original slide content. These divs don't get the slick-active class but for theming purposes this might be required. The following code adds the .slick-cloned-active class to .slick-cloned elements when active.

slick.add_class_to_cloned.js

(function($) {
  // Initialize slick slider on elements having the .slick class.
  var slider = $('.slick');
  slider.slick({
    // There is no reason for cloned divs to appear when infinite is set to false.
    infinite: true
  });

  slider.on('beforeChange', function(event, slick, currentSlide, targetSlide) {
    var $targetSlide = $(slick.$slides[targetSlide]),
        $clonedSlide;
    // The following line will play well if only one slick exists on the page.
    slider.find('.slick-cloned').removeClass('slick-cloned-active');
    if (targetSlide > currentSlide) {
      // Go back.
      $clonedSlide = slider.find('[data-slick-index="' + (targetSlide - slick.$slides.length) + '"]');
    }
    else if (currentSlide > targetSlide) {
      // Go forth.
      $clonedSlide = slider.find('[data-slick-index="' + (targetSlide + slick.$slides.length) + '"]');
    }
    if ($clonedSlide && $clonedSlide.length) {
      $clonedSlide.addClass('slick-cloned-active');
    }
  });
})(jQuery);