With so many people having home theater systems, they are used to preamps that have a subwoofer out. In a regular stereo amp that has no surround processing, if you see something marked subwoofer out it typically means it is a preamp out. In essence nothing more than voltage signal coming from the preamp, fed to the woofer's amp that is then amplified.
So what happens if you don’t have a preamp out? Most every subwoofer made in history is designed to handle that. They have a high-level-in that is hooked up to the speaker taps of your amp. Works the same way. It takes the voltage from the amp as the signal and amplifies it.
This does not cause a power draw on the amp you hook up to. It is using the signal, not the power of the amp to make sound. So there is no “draw” or sapping of power. No negative effect to the sound of the main speakers.
In fact, the most prestigious subwoofers in the industry are made by REL of England. They are the “Gold Standard” of the industry and priced accordingly, topping out at $9,000! Though they can be installed either with line level or speaker level, most REL woofers are hooked to systems with speaker leads of amps.
One snippet of information: Often times subwoofers will allow you to hook them up to the speaker taps of the amp and to cross-over the main speakers, restricting how much low information they get. Don’t assume this is a benefit. It may allow the mains to play louder as they are not having to move as much air, but the downside is you can lose some clarity. Experiment as different products work different ways.