The State of Utah recently passed a law that allows for what's called "free-range parenting." The legislation is more of an affirmation for parents to raise their children within their discretion. "Childrearing" is considered a fundamental right, protected by the Due Process Clause of the 14th Amendment of the United States Constitution. This new law puts that right into practice and is one of the first in the nation. The new provision allows children to walk to school or go to the park unsupervised, if the parent believes that his/her child displays "maturity to avoid harm or unreasonable risk of harm." The law does not specify a required age, allowing prosecutors and judges to make informed decisions about criminal child neglect on a case-by-case basis.
The State of Texas does not have the equivalent legislation but does have a few statutes that make certain behavior around children punishable criminally. For example, it is illegal to leave a child under 7 in a car not attended by someone at least 14 years of age.
A similar Texas statute tracks some of the same language used in the new Utah Statute. Section 22.041 of the Texas Penal Code makes it illegal to intentionally leave a child under 15 in any place or any circumstances that would expose the child to an "unreasonable risk of harm." So, while Texas does not necessarily have the same law in place, Texas uses the same standards when determining what the requirements of child abandonment are.
While most of the legal consequences involving the mishandling of children involve criminal penalties, there is the possibility of children suing their own parents for a civil negligence claim. Generally, such claims of child vs. parent are not constitutionally allowed. As referenced above, parents have a fundamental right to raise and discipline their children. Because of this, parents are constitutionally able to carry out the customary duties attributed to them without the fear of legal consequences.
On the other hand, children can sue their parents for injuries that arise out of conduct that is not customary to a parent's typical responsibilities, like injuries sustained via a car accident directly caused by a parent's negligence while driving.