Extort money, take someone's last penny. For example, That contractor would have bled the department white, but fortunately he was apprehended in time . Presumably this term alludes to losing so much blood that one turns pale (and perhaps also to the idea that money is the life blood of commerce). [First half of 1900s]
tv. to take all of someone’s money; to extort money from someone. (see also bleed.) The creeps tried to bleed me white. These taxes are going to bleed me dry!