Authority is a product of civilization. And we cannot predict what will happen to civilization at such a time scale except in the barest generalities.
However it’s a reasonable bet that by that time, our descendants which will have branched into countless other species would have already colonized other star systems.
Anyone still in the solar system would be well aware of the danger and would have millions of years to prepare. Authority breaks down in natural disasters only if the authority has not prepared or is overwhelmed. So anyone within the solar system would be well prepared and the chance of breakdown of authority and civilzation would be small.