IIRC, Rings uses a “probe” signal to decide whether or not anything is connected to an input, but you wouldn’t normally hear that.
Sockets which are switched (aka have a “normal”, “normalizing” or “normalling” pin - substitute your own spelling), tend to go wrong sometimes, or just get dirt in them, stopping the switch from closing properly, when you don’t have a cable or jack plug, plugged into the socket.
If the switch doesn’t make contact at all, the “normal” connection doesn’t get made when you remove a plug, so the Rings wouldn’t see the test proble signal, would conclude that you have a patch cable plugged in to that socket, and would take whatever votlage was detected as being an actual signal… I guess.
If the switch contact was just dirty, the problem could be stranger - for example, the test probe signal would be more likely to be picked up, but not cleanly, so might not be recognised for what it is, by the firmware. The mangled probe signal would then be used as a signal input, I assume.
In either case, the solution might be very careful application of a switch and contact cleaner, or very careful bending of the spring contact, or it might involve replacing that jack socket.
You could also consider trying a dummy plug or cable, as a diagnostic aid, and as a possible workaround.
There are two main sorts; the simplest sort to try is just a patch cable, with something covering the other end to insulate it, so it’s open circuit but hopefully picking up only a small amount of EM noise.
The other main sort involves shorting the two contacts together, e.g. using a patch cable and temporary use of a conductive metal object, to connect the tip to the ring, at the far end of the patch cable, to act as a zero volt input signal, with less noise. That’s safe for an input, and also usually okay for an output, but less advisable.