120 when it’s not even connected to anything has 120 even plugged in.
2 Answers
There are three possibilities:
This wire and breaker are/were part of a "multi-wire branch circuit", where two breakers and two hot wires (often, but not necessarily, red and black) on opposite bus poles share one neutral wire. When one leg is disconnected from the supply, you can still read voltage (and receive current) through loads on the other leg. Modern editions of the NEC require the circuit breakers in a MWBC to be handle-tied to (a) enforce feeding the legs from separate poles (so the neutral won't be overloaded to 200%) and (b) enforce shutting off both legs at the same time so maintainers won't be shocked if they don't flip both breakers. If you connect a significant load (such as a 60W incandescent light bulb) between this wire and the neutral bus in the panel, it may light faintly or not at all, and voltage measured across the load will be very low.
This wire is somehow accidentally connected to another hot wire from a different circuit on the same phase (connecting to the opposite phase would be a dead short that would trip multiple breakers, or set wires on fire if the breakers fail) somewhere downstream. If you connect a significant load (such as a 60W incandescent light bulb) between this wire and the neutral bus in the panel, it will light at full brightness, and voltage measured across the load will be the same as the open-circuit voltage (~120V).
This is wire is picking energy capacitively or inductively from other current-carrying wires nearby. If you connect a significant load (such as a 60W incandescent light bulb) between this wire and the neutral bus in the panel, it will not light at all, and voltage measured across the load will be zero.
It may not be possible to definitively figure out what's going on just by testing/inspecting in the main panel. It may be necessary to trace everywhere this wire goes.
Side note, Challenger breakers are all defective and should be replaced immediately. They do not trip when they should, which can lead to fires.
Troubleshooting ideas:
Check which parts of the affected circuit also test as energized.
Turn off the main breaker to verify this condition does not exist with the system off. Then turn it back on to proceed.
Turn on only one branch circuit at a time to identify which breaker is powering that wire.
Also of note, there is a white loose wire at the top of the photo.
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The white wire at the top looks like a phone cable it has three tiny wires in it Commented Nov 21 at 9:02