-It depends on the J1 holder. If the J1 holder change employer, J1 and J2 have to do the J1/J2 waiver again. If the J1 holder loses job, the J2 holder also loses his/her J2 status and the EAD based on J2 status is invalid. That is why J1/J2 holder usually change their status to H1 if they can do that or just apply for green card (file i-485).
You have to know nothing is absolutely secure, no matter it h1 or J1, but just say which one is less risky.