You can remove torn wallpaper borders without removing the entire sheet. To do this, use a utility knife with a new blade to cut a sharp, even seam where you want to replace that piece of border. Next, dampen the area with a sponge and fabric softener mixed half and half, and allow it to soak for 15 minutes. Use a scraper to lift up the corner of your cut, and carefully peel off that piece. Use that piece to measure for the new piece of wallpaper border, and place it on the wall.