This depends entirely on the drag coefficient of the train car. If the engines on a supersonic jet cut off, it's essentially a rock traveling at the speed of sound through still air. I don't believe the acceleration is cataclysmic for the occupants (although probably jolting). Remember also that normal commercial gets travel at like 80% of the speed of sound, and they can easily handle a loss of engine power. (Although maybe typical engine cut-outs are more gradual than a suddenly ruptured hyperloop tunnel?)

So the train car need only have aerodynamics similar to an air plane in order to avoid bad stopping forces. An aerodynamic design makes sense anyways since you want to avoid drag.

If the passenger cabin were smaller than the capsule, the cabin's movement could be softened by hydraulic dampers. This could also prevent casualties (e.g. through brain trauma, as often happens in train crashes) in case of an instant halt.

Assuming a constant "engine" output power, which doesn't sound all that unreasonable, the worst case deceleration would be numerically equal, but opposite direction, to the worst case acceleration from a standing start at takeoff.

It's never that bad in practice.

There are much more exciting problems with losing an engine revolving around loss of control.

You point to an important omission in my scientific article! My gut just assumed the reason would be 'drag', specifically reducing it.

I guess the question is: would it require less energy to push capsules/cars through the tube with an acoustic wave than it would to force them through the tunnel e.g. with some sort of propulsion?