If One parent gives up custody, the other has to pay child support.

If both parents give up custody, neither has to pay a cent towards the child.

How is that fair to a person who doesn’t want to raise a child but has to pay child support and how is it fair to the child who is put in orphanage but just gets barely gets its basic needs met with no outside support finacially?

Actually, in some states parents whose children are in foster care have to contribute to their support according to their income. If they lose custody permanently and the children are freed for adoption the support ends.