In the slow cooker, combine the chicken breasts, butter, apple cider vinegar, garlic, and Sriracha. Cook on low for 4-6 hours or high 2-4, until the chicken is fall apart tender. Shred using two forks.
While the chicken is cooking, assemble the slaw. Mix the cabbage and carrots together in a medium-sized mixing bowl.
In a small bowl, whisk together the mayo, apple cider vinegar, sugar, and salt. Pour over cabbage mixture and toss to combine. Refrigerate for at least 30 minutes before serving.
To make the ranch sauce, whisk together all ingredients (or blend in a blender or food processor).
To assemble the sliders, place a small amount of slaw on the bottom of a slider bun. Top with chicken, and then drizzle with ranch sauce. Drizzle with additional Sriracha, if desired. Top with other half of the bun.