The only thing to work out with running a car sub would be putting power to it. A lot of home audio amplifiers are designed for 8 ohm speakers, so if using a sub that is less than that resistance, an appropriate amplifier must be chosen.
A car audio amplifier could also be used with a DC power supply. I used to have four 15" subs hooked up through car amps in my home and it was loud as hell and easy to hook up with power supplies and some old car amps that I had laying around.