The status of a J-1 student, any any J-2 dependent, comes to an end upon:
In brief, once you have completed your studies and academic objectives, as well as any Academic Training, you have a maximum of thirty days to prepare for departure to the U.S. Your status comes to an end when you depart.
You are not required to notify the OIS of your departure, although such notification is appreciated. You are required to notify the OIS if you intend to depart the U.S. more than 30 days before your Form DS-2019 expires.
Teachers College may be required to terminate the status of a J-1 student if the student willfully fails to pursue the objectives indicated on his/her DS-2019. Because this may have serious implications for future immigration benefits, it is essential that you contact the OIS and discuss your situation directly with an OIS advisor.
In addition, failure to maintain health insurance coverage that means U.S. Department of State requirements is a basis for termination of status.