Has there been a pattern of your parents shifting responsibility onto you in other matters? Have they every singled you out among your siblings as the toughest one, the one who can bear the most burden and the one whom they responsibilize (is there such a word?..) the most? When they told you that you should be responsible for the younger sis when they are gone, did they do it just matter-of-factly or they they also try to shame you around this issue? Before your sister dropped out of school and started living in filth, was it the case that you had had more chores at home than she had? Or is this differential treatment purely a result of the shift in your little sister's character and attitude?

Since you now are on speaking terms with her, maybe you may suggest that she has a learning disability and needs help. there are resources and she is old enough to leverage them. Maybe you can help her find the resources as long as it is clear that leveraging them is her duty.