The connections that can be made between the provebs and the folktales is that both of them try to teach something with respect to moral and ethics. They include material culture, life experiences that have been passed from generation to generation. Consequently, folktales and proverbs function as lifelessons. Most of the times, a character goes through a difficult situation and, end in the end, they find the solution to their problem; so they can be taken as a representation of the challenges a culture has to face and provide the people with insight about them.
They might be used to summarize the main conflict portrayed in a novel and also to provide a "hidden" piece of advice indicating that you should do what they preach.