Could be different in each state.

Used to know one fellow who's parent were drunkards. He got the court to relieve his parents' guardian status. This is called emancipation of minor. After that the parents are not bond by law to care for and be responsible for the actions of the minor.

Conditions: the child has to be financially independent, be able to take care of himself. In other words, if these conditions are met, essentially parents can not restrain children from going their own ways. From the example I gave able, these are not that difficult to meet. (That fellow literally slept in the streets for some time before further messed up and became a single father...)