Yes it's a Rem. Model 11
It needs to have the barrel reset into the receiver. The barrel extension needs to fit flush with the receiver. The barrel is out of the receiver just a little. The photo is not clear enough but it sure appears this way. This can cause breakage of parts like the bolt and lock up guides. They maybe broke already. These also have a recoil buffer in the back of the receiver that is riveted in place. W/O this it hammers the rear of the receiver and causes damage to the receiver and internal parts. These are two easily done repairs. To set the barrel correctly you can machine a steel washer down to fit inside the stock and over the magazine tube then the stock can push the barrel back in spec. You can use plastic or build the area up with epoxy but the washer works easy and fast.
The recoil buffer is probably shot to pieces or completely gone. I install these with a little modification to fit over the existing rivet if it is still there. I use Poly Choke adhesive to fit a new one. There are homemade jigs to do these however. The action spring is on the back of the receiver is "plugged" into the tube with a wooden plug. These split in no time and the spring begins to push the plug out of place and then pushes on the stock with constant force. This causes the stock to have space and eventually crack. You can replace the wooden one with one from a Browning A5 as they are made of plastic and will not split. You may have to trim a little to keep it from being "proud" i.e., out of the action tube.
I install the later Browning A5 two piece carriers in these so the carrier button does not have to be held down to load and it can then load into the chamber if the bolt is locked back by inserting a shell into the magazine tube. In other words it will work like the newer (1955 or so) A5 Brownings.
Best way to store is to oil them and loosen the magazine cap or remove it and place muzzle down to keep oil out of the stock and pressure off the recoil spring. These are hard to find. You can get new 15 coil ones and your shotgun may have this kind instead of the 20 coil ones. These are square spring wire. A new one for a Browning A5 can work but it can also jam the action awfully tight. The barrel alignment ring is about 2 inches different on A5 and Rem barrels. You have to know how to modify the Browning spring or install the friction pieces to prevent this. However, sometimes they work W/O any modification.
I order the Choate two shot extensions unassembled, not blued with 870/1100 threads and set them up to work W/O a stock spacer. You can actually get three extra shots if you set this up a little different than normal.