Cord-Friendly Doors

A lot of cords go through my house. Vaccuum cords, drop cords, that kind of thing. I also have a dog, who likes to go outside. I try to keep the doors closed to prevent him from escaping. But whenever I run a cord through my house, the door hangs open when it gets caught on the cord. A door could be made to fix this problem. What you could do is cut off a tiny corner of the door and replace that shape with a piece of weather stripping, or something else flexible. Not just a flap, because you have to worry about insulation, too. And it would have to be large enough so that you could pull more cord through if you needed to. I'm sure that this would keep my dog from becoming roadkill.