You may terminate parental rights after a parent has abandoned a child for more than 12 months without showing adequate excuse or progress to remedy the reasons for the placement.
The grandparent may also be able to bring a child custody action for custody of the child but to be granted custody must be able to prove that both the mother and father are either unfit or have acted inconsistent with their constitutionally protected status as the child's natural parent. Placement of a child with a grandparent for other than a temporary basis could be an act inconsistent with constitutionally protected status.
This is a complex area of law. You should see an attorney.