This assumption bypasses so many factlets as to render it meaningless. For example, none of our decent players will want Third Division football, but with very little bargaining power, those not coming to the end of their contract will be gone for a song. The team will play even bloody worse against the even bigger, even more brutal and even less skilled men in other teams in Division Three, our results will get worse, and attendances will plummet in combination with the pride that will prevent many from watching Div. 3 football.
I am of the opinion that admin will follow relegation as night follows day.