I'd yank it and put in a suitable dorm fridge. They (the dorm fridges) don't hold much but at least you will get whatever you can fit inside cold and won't have to deal with chips (regular or Bar-B-Que) all inside there.
In our old Palomino pup there was a traditional horizontal ice box and we used it for storing delicate items like snack foods, smores ingredients and some canned food at the bottom. We brought along my dorm fridge and set it on a folding table or picnic table under the trailers awning.
2006 23B Hybrid with 10k round bar WDH
2011 F150 4x4 SCREW Ecoboost, Max Tow, Integrated TBC, 3.73 LS axle, Firestone Ride Rite airbags.