Actually, in Faulkner's "A Rose for Emily," Emily has quite a constant relationship with the town. The relationship just stops at Emily's front door. But the house is really a town focal point. The townspeople, apparently, often watch the house and talk about it.
In fact, one of the characteristics of the story that gives it unity is the focus on the house. Almost everything in the story revolves around it.
Of course, Emily doesn't come out of the house much and doesn't socialize at all, but that just makes the relationship of a different kind, it doesn't eliminate it.
Those who enter the home to talk Emily into paying taxes, tell the rest of the town about it. Those who try to get Emily to give up her father's body, talk about it. Those who try to put a mailbox on her home, talk about it. The pharmacist talks about Emily's purchase of poison. The town is almost obsessed with her. This is a relationship, although it's an unusual one.
In short, though, if you need a specific answer, Emily is so isolated from the town because she wants to be and has to be. You don't invite people into your home when you have a corpse of a murdered human being upstairs in your bed--and you're sleeping with it.