Two-channel sub connection options

I apologize if this isn’t a very high-end question, but perhaps my ignorance will amuse you.

I recently retired the full-range speakers I’ve been using with my Integrated Amp and replaced them with some smaller speakers which will require a subwoofer. For want of a LFE output on the amp it appears that I’m obliged to run speaker cables from its System B outputs to the High Level inputs on the sub.

Question #1: Does that mean that some substantial fraction of my two-channel amp’s power will be diverted to the sub, bypassing the subwoofer’s own internal amplifier?

Question #2:  If I simply need a two-channel line-level signal for the sub that is subject to the same volume control as my primary speakers, could I not use the headphone jack on the amp (which has no separate volume control) and run a 1/4" Phone Male to Two RCA Male Cable to the sub’s RCA inputs?

If both of these options are possible, which is preferable?

I'm no expert on this, but I believe the high-level signal received by the sub is converted to a low-level signal before being used by the amplification process in the sub's amp.

I run two subs in my two-channel/HT system by running them off the two-channel preamp using siamese connectors. While this is viewed as being wrong by HT aficionados, it works well for me, as my main focus is two-channel listening.

Good luck,
Thanks, Dan.  That's what I was hoping.  It would be frustrating to have the sub's onboard amp go to waste, while its big driver sucks current the stereo amp should devote to the main speakers.

I wonder why this arrangement is kept such a secret.  I haven't seen anything published about subs explain how they handle high-level signals.
1) Speaker level connections on the sub are a high impedance, so there is minimal current (and thus, power) drawn from the amp.

2) I believe the headphone jack is expecting to see a quite different impedance than that of the line level connections on the sub.

If your integrated amp has preamp outputs (some do), then you could use those to connect to the line level inputs on the sub.
Ok, that makes sense.  I had no idea how the high-level connections could gather the information of the signal without drawing the same current as speakers would.

I had a hunch the headphone jack wouldn't work, or else it would be a known option.

My  Marantz integrated amp does not have preamp outputs, but I'm fine with the line level connections, just as long as the sub's internal amp will still be doing the heavy lifting.

The voltage level across the speaker terminals of your amp is the same regardless of the impedance of the load, i.e., speaker or sub. So when you adjust the volume level of the integrated amp, the voltage across the speaker terminals changes accordingly and the SPL of the speakers and sub will change in direct proportion to that voltage change. The speakers having a low impedance compared to the sub will draw almost all of the current (and power) from your amp; the sub will draw some current, but it's negligible compared to that of the speakers.

The critical issue is matching the SPL levels of the speakers and sub. It's hard to do this by ear, but test tones and an SPL meter make it fairly simple.

That makes perfectly good sense - I just couldn't find it explained elsewhere,

I  have a SPL mater I used to balance my HT system.   

Thanks for your help.
If a REL sub is used as most people prefer (high level from a power amp speaker output), the amp "sees" a 100,000 ohm burden, which is a lot like nothing at all. I use 2 RELs on the same power amp with the main speakers on the same output…works very well…(resulting in a 50,000 ohm load maybe) both RELs sum the stereo mix as one of the subs is stuck in a window for deck sound occasionally. This allows the main speakers to work as designed, which could be better than shelving the bass with a crossover as, again, they likely weren't voiced for that…but can still sound fine I suppose. I don't bother with an SPL meter for the RELs to match the mains somehow, as they are turned up and down a bit relative to my taste, the amount of bass energy in a recording, how much Irish whisky I've consumed, and if my wife can be compelled to dance with me. 
Those strike me as perfectly legitimate criteria for setting your preferred bass level.