An International Student in J-1 student status who is 'making normal progress towards degree completion and remains enrolled full-time - but who is unable to complete his/her course of study' by the expected completion date on your DS-2019 may be eligible for a program extension.
You will need to meet with your academic advisor to review your program objectives and if academic advisor recommends an extension for you to complete yoru degree then you will complete the necessary form. Once this has been completed - submit to the ISSO for review and if approved a new DS-2019 will be issued to you .
Please note - in order for a program extension to be approved there must be a compelling academic or medical reason. If there is no compelling reason for the extension then you must complete by the date noted on your DS-2019.
This extension must be processed prior to the date on your DS-2019 or else you will be out of status.