JK's answer is most similar to what I had in mind. When I rap with a haul bag I typically put the bag on rappel on an extended sling clipped to the rappel device, then clip myself to that 'biner with a separate 'biner. That setup would make it very easy to escape the haul bag by just adding some stopper knots below the belay device, attaching yourself to prusiks above the device, then unclipping and jugging the ropes on the prusiks. You could then haul the bag to the anchor using either strand of rope.
In my real world similar situation, my partner was doing a double rope rap with the haul bag, and ended up hanging in space about 80' down, with a set of anchors on the wall in front of him (but out of reach). He could have kept rapping to where the ropes came back in contact with the wall, but we weren't sure if he would find another rap station, and the blank face didn't offer many options for a gear anchor. It was also dark.
He tried swinging into the wall but it was tough to get enough momentum going. From the anchor above, I ended up prusiking down the ropes to where they came free of the wall, and from there I could push/pull the ropes to help him generate a swing. He was eventually able to snag the anchor and then everything was back to normal.
But of course it got us brainstorming other solutions. Our next move would have been to get him and the haul bag back to the anchor as described above, then rap without the haul bag (should have done that the first time), which would make it easier to swing to the anchors below or explore further down for another rap station. Cutting the pig loose definitely came to mind ;)
Thanks for the replies. I realize the question was a little vague and open-ended, but I enjoy hearing different ideas for potential solutions. Has anyone else encountered a similar scenario?