You can rent out your male pig to other owners. When you move a pig from the Pig Pen to the Pig Plaza, you can choose whether you want to allow pig rental for that pig.
If you want to change the settings after the pig has been sent to the Pig Plaza, you can do so from "Male Pigs" from the bottom right in the Pig Plaza.
When other owners rent out your male pig, you'll receive points as a rental fee. The rental fee varies depending on type.
Your male pig will come back after a certain period of time, and you will then be able to ship it.