Could it be a wired doorbell chime?

If it's a doorbell that front cover should lift off. Then post a photo of the guts for more specific answers.

It is almost certainly a doorbell chime. Do you have a doorbell button?

Most doorbells run off 16 volts, so they are powered by a transformer somewhere on the other end of that wire. The transformer may be near your electrical panel, or they may have attached it to receptacle somewhere else in the house. If its still there and working, it will be accessible because it has to be connected to 120 volts also.

The cover should pop off the base, and there will be two screw terminals. You could use that connection to measure the voltage. If the wires have no power, regardless of pressing the doorbell or not, it is likely that it is no longer connected to a transformer. However, if it still has power, you need to track down the transformer and disconnect it, then just push the wires back into the wall.

Bruce

Looks pretty much like a whole lot of doorbell boxes I have seen, and no you cant snip off the wire, it is probably a hot wire. Does your doorbell work? In any case, I would just leave it there, and enjoy it. If you have a doorbell and it doesnt work, then buy a new part for the doorbell, and see if that fixes it. They are about 5.00 or so for the new doorbell part at Lowes, or Home Depot.

If not a doorbell a intercom system possibly between two floors or different parts of house. If it's up high near the ceiling most likely a doorbell.

It's 100% either what klem1 said or a doorbell.

It's a little hard to tell exactly what the wire is in your photo, but it looks like light gauge wire encased in a jacket...the kind that is typically run from a transformer to a device like a chime. Could be 2 or more wires (but likely only two connected). If this is a standard low voltage circuit -- not household 110V -- you can just abandon it in the wall: you don't need to terminate it in a box as was suggested above, and then and patch the wall and install your shelf. The fact that there is no box there now suggests that this is low voltage.

It makes since that it is a doorbell box. It is near the side door of the house. There is a doorbell outside this door, but it is no longer working.

I would repair the doorbell. Its nice to have a working doorbell. You can get a new exterior wired one for about 5.00 at Lowes.

Note the screws from the device into the sheetrock. They had to be tightened from inside the device when installed.

The OP needs to smarten up and figure how to remove the cover - likely snaps on.

If not, break the plastic case. If there is voltage still present, you may have a salvageable doorbell at that side door.