In an instance such as major earthquakes, globally, such as those that will accompany the rotation stoppage, it is like a disaster ramped up into a larger
scope. The same processes occur: all the hospitals are mobilized, people are ferried out of the disaster area to safer places, tents are erected, looting is
suppressed, and this is done on a larger scale. In situations such as this, there are more people that are unattended, ill, but unattended. A broken leg
sometimes for days before being set simply because greater emergencies exist. So it is just a matter of scale.
Why would Martial Law be imposed in the face of an emergency such as this? Rather, all of the emergency personnel or volunteers would work themselves to death as they did in the 911 disaster at the WTC, without stop. This is how they would react. Martial Law is only imposed in rare circumstances in democracies or in social democracies where it is only a short delimited and a disaster does not already exist.
Therefore, worry less about this than about your neighbors. We will tell you that a mass disaster, such as seeing an object in the sky, accompanied by large earthquakes and a communication shutdown, is going to cause your greatest worry to be your neighbor or someone in your household. People will go mad, they will go insane, they will be frantic with anger and wanting to direct it somewhere. They will be lashing out at each other. They will run away from their responsibilities and then be dealing with grief on top of anger. You should expect, as you do with animals that go a bit nutsy during an earthquake or prior to an earthquake, you neighbors and family member may be unpredictable, angry, lashing out. Anticipate this, and formulate an action plan to deal with it, and do not be surprised.