How does a garlic clove thrive inside a closed refrigerator?
Your garlic was likely purchased as a bulb, not seed, and stored in the fridge.  The garlic 'clove' is not frozen, so your fridge readily mimics underground conditions in the temperate late winter or spring season. The bulb is generally buried underground, and the subsequent initiation of plant development and growth uses the stored energy. In a garden, the garlic would, however, begin photosynthesizing soon thereafter. Bad news: in your fridge, the plant is certain to become etiolated, because the lack of light, and yes, eventually run out of the stored resources--and die. Good news: you can eat or transplant it.