no longer wants to live with the parent that has sole custody

The answer would depend on where the child could live as an alternative to the parent with sole custody. It would also depend on the age of the child.

The child's best ally in such cases is generally the non-custodial parent. Said parent can usually take charge for the child and petition the courts for custody if the change is contested by the other parent.

If the child is old enough and if the situation warrants it, he or she can also seek the help of an attorney who can act on his or her behalf.

If there is no other parent capable of taking care of the child, and if the child is in a situation involving abuse or neglect, the child can always communicate with Youth protection services or someone in his or her milieu, such as a teacher, who could help guide him or her to the most adequate resource.