Simply, the refrigerator would STOP! but why? To answer this question, one needs to know the Second law of thermodynamics (Clausius Statement) which states “It is impossible to construct a heat pump which continuously takes away the heat from low-temperature region to high-temperature region without taking any external work”.
Here, the heat pump is our refrigerator which keeps on throwing heat from low-temperature environment to room temperature. As per the above statement, external work is a must to run the refrigerator. That external work is represented by the “Compressor”.
Second thing, to have heat transfer from the evaporator to the condenser, you need to change the phase of the substance. The change of phase absorbs or liberates the heat depending on the phase change. Thus, the heat of food can be transferred to the condenser by changing the liquid phase refrigerant to the vapor phase in the evaporator and this heat is rejected at the condenser at room temperature. This task is performed by the compressor by changing the pressure of the refrigerant.