回复：Please refer to wording below - 回复：Updating DS-2019 of J-1 do

May I still work if the status of the J-1 ends? If the J-1 visitor discontinues the program at Columbia or changes to another visa category, the work authorization for the J-2 dependent will be withdrawn. Legal work authorization for J-2 dependents is always dependent on the status of the J-1 principal.
-I also noticed that what you emphasized. Bu the confusing meaning in this paragrahp is that "discontinue the program in Columbia..." because even if you do not finish your J1, but you leave Columbia, you can be considered "discontinue the program ...". So, it seems the J2 EAD may be the J1 sponsor related.