What are the chances of a grandparent getting custody of a grandchild from unmarried parents who are endangering her by not tending to her well being?

There is no "percentage rate". The court is concerned with the child's welfare only. If someone believes a child is endangered or being neglected, they should report it to CFS. An investigation will be done, and if the claims are proven true, the child(ren) will become Ward(s)of the Court. A custody hearing will be held in Family(Domestic) court. Grandparent(s) are often granted custody if they are willing and proven able to care for the child(ren).