Think about the application rather than the procedure. In the real world what would really happen? Anything is the answer, and every ATCO across the world will be trained with this in mind.
There are so many ways and means of understanding a problem and knowing what the next move is, watching Mode S to see the level select, heading select etc, squawking 7600, sending messages to company, Sat Phones, or if losing RTF is a feature of failures, watching everything failing (ie Mode S or elements of it all the way to total transponder failure).
Whatever the circumstances, I can imagine a pair of escorts will be soon on the scene and every other track in the vicinity will be vectored elsewhere, it almost doesn't matter what you do in the cockpit, because you'll be the only one in your piece of sky anyway.