I am not making my point very well, or maybe I am mistaken in thinking I have a point. Let me try again.

The proposition is that eventually evacuees or refugess can become themselves a disaster or emergency in the areas to which they flee. If you find the proposition nonsensical, then we can agree to disagree. If you can see the proposition might come true, then let us discuss its ramifications on preparedness.

To be as specific as I think is necessary:

The event is whatever would send a wave of millions of refugees / evacuees into your neighborhood.

The place is your neighborhood.

The time of year does not matter for the basic question, but can be posed for each time of year for purpose of discussion. I suppose the dead of winter would pose the greatest challenge.

The precise number of refugees / evacuees is whatever number would exhaust the resources of any organized response in your neighborhood.