I had a similar issue. They hooked the sub into an existing speaker (y connection) - and then added a filter to remove the higher frequencies before sending the signal to the sub amp. Worked fine. The whole unit (sub box. amp, filter) was mounted in the back of a VW Passat - using the factory system.
I used the sub to subliment the bass - but when it first came back from the installer, it was setup to shake the world. I turned down the amp and it ended up mixing correctly. So, if you are looking for that "shake the car next to you" solution, you can do that as well...
Even though this forum is for home theater and music subs, the traffic is light. So anything to keep it going.
You need a LOC (line out converter). It will take a speaker level signal and lower it to a line level signal. I added a 12" Soundsplinter to a friend's factory stereo system in a Dodge Magnum. I tapped into both of the rear speakers and used a Scosche LOC from Wal-Mart. It fed a Phoenix Gold Tantrum (500w mono) which pushed the 12. I installed it in a Schosche pre-fab box from Wal-Mart. Not the best enclosure but if you glue it together, it's better than nothing. It met his budget and time requirements. With a little bit of tweaking, the sub really added the low end punch that was missing from the factory stereo.
I will be doing something similar in my wife's Lexus ES-350 soon.
If you can, it is always better to replace the head unit with an aftermarket model. Even the cheap ones are better than the premium sound systems that come from the factories.