It probably depends on the type of fridge or freezer. I converted a standard (Sears Kenmore) 9cf chest freezer to an energy-efficient refrigerator by adding an "external" thermostat that was supposedly designed for homebrewing. The long probe of the thermostat is inside the freezer and the control unit is in a box on the wall along with a split 2-outlet AC socket: if I plug the freezer into one outlet it runs as a freezer, in the other it runs as a refrigerator at about 35-40F. In the latter mode, with ambient temperature about 60 (in the basement), my Kill-a-Watt meter says it uses about 7 watts average.
But there are issues: This chest freezer has the cooling elements built into the inside walls and, when it is running, those wall get below freezing. Thus I have to keep sensitive items (veggies) a bit away from the walls. And, I get condensation on those walls, especially in the summer (more humid), despite the limited air exchange with the basement due to the chest style. After some time it collects quite a puddle on the bottom, and it started rusting. Thus I need to keep the contents off the floor of the unit, and sponge out the water every month or so. This is definitely not what it was designed to do, although with care it is still useful. With a minimal PV system it was all the frig I could run in case of a grid outage (along with a chest freezer and some lights).