The only thing I can think of is that somebody rents space in his fridge; then (perhaps) a group of people pay as they use the space (room).
Problaby the person means that there´s a system in which you can rent space for the night, and there´s the likelihood of somebody paying for the rent for the price of piece of cake.
That is, for peanuts - a "stealing" (bargain) like they say. But then, assuming a piece of cake is not expensive in the area!
In other words, I understand it as "buying storage room". It wouldn´t be a common event in the so-called developed world, but then one never knows! Plus, the sentence comes from elsewhere, so no context available. So, the developed world thing is just a passing comment.