Sounds like it could be a plate adapted for either phone or internet, but without the connector in place. It could perhaps have been pushed out of position, or perhaps never seated properly.
The thing to do is remove the plate from the wall and see if anything's behind it. If there's a phone connection, it needs to be seated or glued into position so that the phone cord can be inserted from the other side.
One of these days we'll have a small robot that someone can move into and operate by remote control. Then we tinkerers can visit our neighbors and fix things for them.
I'm sure that's coming but first the motivated engineers over at the porn connections have to figure out the right way to create the feedback loops. Once they do that they'll become gazillionaires, but they haven't contacted me about it yet.
Nothing in the hole. It looks like whatever (”phone clip?”) was in the hole was removed, and possibly forcefully. So my plan at the moment is that some day, when I feel like moving the dresser and the night stand (solid wood and very heavy), I’ll watch a video to refresh my memory, then take notes as I remove the jack from the bedroom and put it into the living room.