I've just discovered what looks like some crazy wiring. Our basement staircase has a light at the top of the stairs and a light at the bottom, as well as 3-way switches at both the top and the bottom. The 3-way switch at the top of the stairs was damaged by the tenant in the basement so I went to replace it with a new one making sure I connected all the wires as they were previously. When testing, I realized the two lights don't operate at the same time and the top light is not controlled by the bottom switch, so I decided to investigate and figure out how they were wired.
It looks like the bottom light is correctly wired for 3-way operation, but the top light is simply connected to the black and one of the brass screws in the top switch, such that it is effectively using the bottom light fixture as a neutral.
I've attached a diagram which I'm pretty sure is accurate.
Edit: and here's my attempt at a wiring diagram
FYI: the top light is an LED fixture and the bottom light is a regular lamp/bulb fixture. When the top light is on and the bottom light off, I read 12V on the hot wire of the bottom light.
Is this allowed or even safe, and if not what is the best fix?
Whoever owned this house previously seems to have done crazy stuff all over the place.