Didn't something like that already happen when the whole Governing Body in the sole person of C.T. Russel, died? Remember there was a power grab by Rutherford where he dismissed and demonized some of the individuals who Russel appointed and who were seeking to follow Russel's directions in his will.
I think something similar could/would happen. A power hungry brother or brothers in the legal dept will seek to wrest power unto himself/themselves and expel and demonize all who refuse to submit to their power grab. There might even initially be some secret political lobbying among prominent competing brothers in the legal dept. and/or the writing dept. to see who can muster the most support to form a coalition government ... I mean ... Governing Body to govern the organization.