J-1 students are allowed an additional 30-day grace period after their program completion date to prepare for their departure from the U.S., transfer to another U.S. school/degree program, or change their visa status in the U.S. During the grace period, employment or full-time study is not allowed.
Upon departure from the U.S. during these 30 days, the J-1 visa status automatically expires and you will not be able to re-enter the U.S. to reclaim the rest of your grace period time.