Salt depresses the freezing point of water. When you freeze salty water, the behavior depends on whether you’re at, above, or below the eutectic point, -21.1° and 27% NaCl. If less saline than the eutectic point, first you get ice crystals sucking up heat and growing without much salt until the remaining brine is at the eutectic point, at which point it freezes. If more saline than the eutectic point, instead you get salt crystals sucking up (much less) heat and growing without much water until the remaining brine is at the eutectic point, at which point it freezes.
On the other hand, if you have salty ice and you melt it partway, the part that melts first will be the eutectic phase, leaving the remaining phase (either water or salt) more concentrated in the remaining crystals. At this point you can mechanically separate the two with an arbitrarily small energy input.
I was thinking that you could use this behavior somehow to get a refrigerator, but now I’m not sure you can. It seems like the movement of mass into the eutectic phase is kind of unrecoverable by freezing and melting. Maybe you could separate them with a pressure swing or by distillation.