"The wool is on the dog, and the pig pays the bill" is an idiom, which means that a person or a party first does something for others or other parties, and then others or other parties bear the responsibility or pay the price. This idiom is used to describe some people or organizations who use others or other parties to obtain benefits or benefits, but they do not bear the responsibility or cost.
Among them, "the wool is on the dog" means that a person or a party uses the labor or resources of others or other parties for the purpose of obtaining benefits, which is similar to shearing wool for dogs. The "pig pays the bill" means that someone else or the other party bears the responsibility or pays the price, which is similar to the pig paying the bill.