As with the other "advocate" positions raised earlier, one does not need a law degree to be a patent agent. A Bachelor's will do just fine. In other words, you don't need go through the time, energy and expense of law school in order to be an "advocate." If that is your end goal, then you can get started on that path now and skip the J.D.
If the goal is to become a patent agent or SSA advocate, then spending money on a JD probably does not pass the cost/benefit analysis. I believe the OP's intention, however, was to point out career options for DL students who do not pass the bar.
Let's say you get an online/correspondence JD, take the bar a few times, and realize that it's not going to happen. Is there a way to utilize the knowledge and make money? Perhaps.
Although a JD is not required for these careers, knowledge of statutory construction, civil procedure, and maybe conlaw is useful. In that way the JD holder can enhance their abilities and be a better patent agent, SSA advocate, etc.
I don't think the OP was suggesting that anyone obtain a JD in order to become an advocate, or that they become an advocate in lieu of professional licensure.