A passive sub means it's just a loudspeaker in a box. Loudspeakers - just like your main bookshelf speakers - need an amplified source otherwise you won't hear any sound.
A single speaker in a box is mono, not stereo. That's going to be another challenge; getting a stereo amplifier to drive a mono speaker without either losing some sound or blowing up the amp due to signal feedback. Besides this though you have a bigger problem in blending the passive sub so that it doesn't mask over the bookshelf speakers. Hi-Fi subs do all this because the sub has an amplifier built in, and it sums the stereo signal to mono safely, and it provides controls for sub volume, phase and crossover frequency.
In all honesty, unless this passive sub is something really out of this world, you're much better off selling it and buying a proper active subwoofer with high-level (speaker level) inputs to go with your stereo amp and speakers. And if this passive sub is from an old home surround kit that gave up the ghost, but you thought you'd try to use it with your new gear, then stop now before you waste your time, our time, and a bunch of money trying to polish a turd.
Look for a used BK Gemini II or BK XLS200 subwoofer. Both have the ability to run from the speaker output of your amp without affecting the way the main speakers work. It's a neat trick and perfect for someone with a simple stereo amp. There's only one caveat. Your amplifier must not be a Class D type. More specifically, you can only use a class D amp if it goes through a special adapter that protects the sub input circuit from the high ground level of the amp. That's a bit technical I know, but trust me, it will stop you burning out the input stage on the sub after 50 hrs use.
You'll have the same issue with any active sub of any brand if it supports a high level input, so don't think of this as just a BK issue because it's not. It's an amp issue, but only on Class D. You're perfectly safe with Class A/B amps.
