The short answer to your question is "yes" it is certainly possible to use a car woofer in a home system. The problem that you run into is that the automotive environment requires a much different woofer than a living room and are designed as such. Because of that, you seldom find any divers that will truly work well in a home setting. I do know of a woofer that will work well in this box, beware, it is likely that you will need to seal your vent/port. Try it both ways. It is a Tonegen 1259/NHT 1259/Madisound 1259. Tonegen manufactured this woofer and NHT used it, then a couple of people knocked it off, the most notable was sold by Madisound.
I noticed someone selling one on ebay as a NHT 1259 replacement.
Good luck, these will work well. Tim