Your grandmother needs to hire a lawyer and sue the birth parents to obtain a custody order. She has nothing to prevent either parent from taking the child.
The author of this opinion is licensed only in the states of NC, SC and TN.
I agree with Mr. Kelso, she should consider bring a custody action. Without a custody order in place, the child's mother and/or father have a constitutional right to the care, custody, and control of the child. However based on the very limited information, it sounds like they have acted inconsistent with that right, and that it may be in the child's best interest for his custody to be with grandmother.
Any answer provided through this discussion board is a general response to the question and NOT intended as legal advice. Responding to this question does not constitute an attorney-client relationship. Always seek the advice of a lawyer directly to address your specific circumstances.
Sign up to receive a 3-part series of useful information and advice about child custody law.