Older Characters In The Outsiders

I think a simple answer to your question is yes. Although some stories may cast aside the older characters or not even include them in the first place, there are some stories where the mother or father character is an important part of the overall narrative and even drives the story forward. In stories where there are a lack of older characters, there is usually a character that can be singled out as an "adult" character even if they fall into what we consider the YA range. In The Outsiders for example, this was the character of Darry. He's supposed to be a greaser and everyone considers him to be one, but with his level of maturity and age he is elevated to something more.