A sponge is characterized as “readily absorbing fluids and yielding them on pressure.”
It is the latter part of this that led to one of the slang senses of sponge, the noun, “an object of extortion,” and the verb, “to deprive one of something.”
It is this meaning of extortion that resulted in the coining of sponging house, sometime in the sixteenth or seventeenth century, as a slang name for the house (usually the bailiff’s home) in which men arrested for debt were held overnight prior to being led off to debtors’ prison.
The reason is that the bailiffs made a good thing of this.
They charged exorbitant prices for food and items of comfort given their prisoners, pocketing the profits, and also took advantage of their wards’ temporary quarters to try to pry from the prisoners’ friends either payment of the debt or further tribute intended to ensure the comfort of the “sponge.”