Powered subwoofer connection?

CHECK OUT REL SUBS - besides the LFE input they use a Neutrik connection which attaches directly to your speaker outputs of your amp...this works very well for integrating with the mains.

"It may also be possible to run a set of speaker cable from the amp to the preamp."

oops, I meant to say... run the speaker cables from amp to sub.

Are powered units available that run off your amp?

Yes.
A powered sub has its own internal amp with volume and frequency crossover controls.
Most subs have RCA inputs that your preamp feeds, some subs have both RCA and speaker wire connections. When you use the RCA inputs, your Volume Pot controls both the main spkrs and the subwoofer together. This is the easiest setup.

Tell us what amp you are using. It sounds like you are using an integrated amp, if so is there a preamp output on the back?
It may also be possible to run a set of speaker cable from the amp to the preamp.