I leaned on the tub spigot and it broke off, revealing a completely rotten pipe underneath. I think that the previous owner may have actually glued it to the bathroom tile with caulk. Fortunately, my diverter valve is in the wall, not attached to the tub spigot.
So this rotted pipe is just sticking out of the wall, but I don't know if I can even unthread it from the elbow where it attaches because it's so corroded. This is definitely a bonus chore. But it could grow since the advanced state of decay suggests that I need to replace all my original 1954 galvanized plumbing sooner rather than later.