What is the name of your state (only U.S. law)? FL
In Florida, can an adoptive parent change their mind after an adoption is finalized? Is that adoptive parent allowed to adopt the child back out to another family?
Typically, once an adoption has been finalized the adoptive parent cannot "undo" the adoption.
However, once an adoption has been finalized, the adoptive parent becomes a legal parent with all rights and responsibilities, which include placing the child for adoption as long as it is done the correct way through the required legal channels.
If this is what the adoptive parent is wanting to do, that parent NEEDS to get a consult with a local attorney before doing anything.