Oh how awful.
Speedy - can I ask how you trained your dog not to run out?
It takes time and you must devote several weeks to it, start by having someone hold the dog on a leash while you open the door and the dog can see out, but can't go out while on the lead. Tell him/her to stay. (BTW, EVERY dog, no matter how little, should have a collar and leash or a harness and leash. Make sure they are in the harness or collar correctly when training!) After a few seconds, say "Okay!" in an upbeat voice and allow them to go out with you.
Keep doing this. Lengthen the time in which they need to stay, and then always reward them with a happy "OKAY!" so they can go out to you.
After a few weeks of this, instead of the leash, tie a heavy string or better yet, a light line, which can be as simple as a heavy duty strand of fishing line. The idea is for it to be very light so the pup thinks he's not restrained. Continue the same lesons...
Stay, Okay. If he tries to go through the doorway before you say Okay, pull back on the lead. This is where teaching your pup to "Sit" comes in handy... he can't Sit and Walk at the same time!
After you are positive he's got that down, introduce something that you think will make him break through the door, like another dog, someone else the dog likes, a toy... again, STAY! and when he does for the set amount of time, reward him with being able to go through.
Within about two months time, if you've done this right, he won't step through the doorway without the Okay from you. I think this is one of the most important things you can teach a small dog, since it will save their lives. My two will stand there at the threshold and watch what's going on, but unless I say Okay, they will not step one foot outside. This is really important, especially with my big dog. She LOVES kids, and there are lots of them around here, but some are scared of big dogs. It's nice to be able to open the door and not have to need to keep a 120 pound dog inside while I sign for something or chase off a salesman.