The Twilight Zone - Nothing In The Dark

The old Ms. Wanda Dunn is afraid of Mr. Death, and does not open the door of her room for anyone who knocks the door. When the police officer Harold Beldon is shot at her front door, the reluctant woman opens it and lets him in. She helps Harold and she tells him about her fear of Mr. Death and that her time was coming, therefore she could see him. When a contractor comes to demolish the building, he explains the "old gives space for the new" to her and she finds that her new journey has begun