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For one it would sound lke crap. Second you would fry it. It needs air to stay cool.
I have seen ported subs that can be done like this, "But" they never over drive them. They also have a small port on the rear to help keep the air moving on both the front stroke and return.
The factory Ported boxs for a 10" 300 watt RMS sub is still 1.6 Cubic foot, for best sound.
Listen to Muffinman, he knows what hes talking about. Its do-able, you can make it very small without blowing it, however you would have to set your gains just right and make sure not to overpower them, smaller than recommended enclosures kill power handling on subs. If you were to make it too big your sub would begin to act as if it were in free air, you would get very very hollow bass and wouldnt be able to tell if you were distorting your sub or not. Now you dont have to be dead on with your box designs, generally you can float around within a good .3 of the recommended and be ok, sealed boxes are pretty forgiving, however build it as close to manufacturers specs as possible, and dont forget driver displacement. Maybe look for a sub with a smaller enclosure size.