I already had the wall open as part of the remodel, along with the wall
I was moving it too. It had to be moved, so the only advantage of
tracing the circuit would have been to turn off a single breaker
instead of the main, or avoid splicing a dead wire. Since it appears
to be original wiring I am 99% sure it is powering something somewhere.
Didn't feel like moving insulation or basement ceiling tiles to figure
it out.

The two screw clamp connector is the type I used.